This week, Diamond Jim Tyler demonstrates a new take on an old trick. Regular Grey Matters readers won't be surprised to learn that I like it because it's based on math, and it's very counterintuitive. We'll start with the new video, and then take a closer look at the trick.

This week's Scam School episode is called The Collective Coin Coincidence, and features Diamond Jim Tyler giving not only a good performance, but also a good lesson in improving a routine properly:



Brian mentions that this was an update from a previous Scam School episode. What he doesn't mention is that you have to travel all the way back to 2009 to find it! The original version was called The Coin Trick That Fooled Einstein, and Brian performed it for U.S. Ski Team Olympic gold medalist Jonny Moseley. It's worth taking a look to see how the new version compares with the original.

Brian and Jim kind of rush through the math shortly after the 4:00 mark, but let's take a close look at the math step-by-step:

Start - The other person has an unknown amount of coins. As with any unknown in algebra, we'll assign a variable to it. To represent coins, change or cents, we'll use: c

1 - When you're saying you have as many coins (or cents) as they do, you're saying you have: c

2 - When you're saying you have 3 more coins than they do, the algebraic way to say that is: c + 3

3 - When you're saying you have enough left over to make their number of coins (c) equal 36, that amount is represented by 36 - c, so the total becomes: c + 3 + 36 - c

Take a close look at that final formula. The first c and the last c cancel out, leaving us with 3 + 36 which is 39. If you go through these same steps with the amount of coins (in cents, as it will make everything easier) as opposed to the number of coins, it works out the same way. This is what Diamond Jim Tyler means when he explains that all he's saying is that he has $4.25 (funnily enough, he says that just after the 4:25 mark).

As long as we're considering improvements, I have another unusual use for this routine. If you go back to my Scam School Meets Grey Matters...Still Yet Again! post, I feature the Purloined Objects/How to Catch a Thief! episode of Scam School, which I contributed to the show. It's not a bad routine as taught, but my post includes a tip which originated with magician Stewart James. This tip uses the Coin Coincidence/Trick That Fooled Einstein principle to take the Purloined Objects into the miracle class! I won't tip it here, so as not to ruin your joy of discovery.

Something about the challenging nature of calculating compound interest keeps drawing me back, as in my Mental Financial Wizard post and my recent Estimating Compound Interest post. Or, maybe I'm just greedy.

In either case, here's yet another way to get a good estimate of interest compounded over time. It's a little tricky to do in your head alone, so you'll probably prefer to work this one out on a sheet of paper.

It turns out that compound interest is based on the binomial theorem. This means we can use relatively simple math concepts from Pascal's Triangle (also based on the binomial theorem). The method I'm about to teach you has its roots in the approach used to work out coefficients in The Easy Peasy Binomial Expansion Trick (jump down to the paragraph which reads, "So now comes the part where the coefficients for each term are written. This is very easy to do with the way we set up our example.").

What we're going to be estimating is the total percentage of interest alone. Once this is done, you can calculate the original investment into the problem. As a first example, let's work out 5% interest per year for 10 years. To keep things simple, we'll work with 5% as if it represented 5, instead of 0.05.

To get a starting point multiply the interest rate by the time, as if you were working out simple interest. In our 5% for 10 years example, we would simply multiply 5 × 10 = 50. You need to make a table with that number expressed two ways: As a standard number, as as a fraction over 1. For this example, the first row of the table would look like this:

Someone invested $2,000 in a fund with an interest rate of 1% a month for 24 months. Consider it to be compounded interest. What will be the accumulated value of the investment after 24 months?

A) $2,437.53
B) $2,465.86
C) $2,539.47
D) $2,546.68
E) $2,697.40

A recent question on the Mathematics StackExchange about mentally the compound interest formula caught my attention.

It got me thinking about good ways to work out a good mental estimate of compound interest.

Part of what makes it so tricky, is that compound interest doesn't work in a straight line, like much of the math with which we're familiar. Compound interest builds on itself exponentially (not surprising since the formula is a exponential expression). This is a good point to re-familiarize ourselves with the basics of the time value of money:



For a more detailed guide to interest rate mathematics, I suggest reading BetterExplained.com's A Visual Guide to Simple, Compound and Continuous Interest Rates.

BINOMIAL METHOD: The Mental Math wikibook suggests the following formula: To estimate (1 + x)ⁿ, calculate 1 + nx + ^n(n-1)⁄₂ x².

It is an interesting formula, especially considering that the first part, 1 + nx, is basically the simple interest formula. However, after using Wolfram|Alpha to compare the actual compound interest rate formula to this binomial estimation of compound interest method, you see that it really only gives close answers when x is 5% or less, and n is 5 time periods or less.

If your particular problem qualifies, that's not bad, but what about longer times?

RULE OF 72 AND OTHERS: Last July, I wrote another post about estimating compound interest discussing the rule of 72 for determining doubling time, as well as the rules for 114 (tripling time) and 144 (quadrupling time). Note especially that you can work out the effects of interest of long time periods with a little simple addition.

Yes, the rule of 72 has been explained many places, such BetterExplained.com's Rule of 72 post, and critically analyzed, such as MindYourDecision.com's Understanding the rule of 72 post and the related video, but as long as you understand its proper use and caveats, it's an excellent tool.

Understanding where the rule of 72 comes from, you can actually work out other rules for other multiples of your original amount, which is how the rules of 114 for tripling and 144 for quadrupling came about. If you want to estimate how long your money takes to grow to 5 times the original amount (quintupling), there's the rule of 168. Similar to the other rules, you can work out quintupling as ¹⁶⁸⁄_time ≈ interest rate (as a percentage) and ¹⁶⁸⁄_interest ≈ time.

To help increase the accuracy of needed estimates, you can also remember the 50% increases between each of the above rules. For a 50% increase, for example, there's the rule of 42. For 2.5 times, there's the rule of 96, for 3.5 times, there's the rule of 132, and for 4.5 times, there's the rule of 156.

This may seem like too many rules to remember, but there are a few things that help. First, keep the rules of 72, 114, 144, and 168 in mind as primary markers for 2×, 3×, 4×, and 5× respectively. Note that these are all multiples of 6, and that the “half-step” rules are also multiples of 6, and fall between the other numbers. So, if you forget how to work out 2.5×, you can realize that the rule is somewhere between 72 and 114, and then recall that 96 is the rule you need! Here is a handy Wolfram|Alpha chart for which rules go with which amounts.

“RULE” EXAMPLES: In the video above, Timmy needs to find out how long it will take to get 10 times his money at a 10% interest rate. Since we only have rule up to 5, how do we work this out? Well, 10 times the money is basically the same as quintupling the money, then doubling that amount of money. So, we can work out the quintupling times and doubling times at 10%, then add them together!

For quintupling, we use the rule of 168 to find that ¹⁶⁸⁄₁₀ ≈ 16.8 years. Since these are estimates, you can usually round up to the nearest integer to help with the accuracy. So, his money will quintuple in about 17 years. How long will it take to double from there? We use the rule of 72 for doubling, so ⁷²⁄₁₀ ≈ 7.2 years, and rounding up gives us 8 years. Since it will take about 17 years to quintuple, and about 8 years to double, then getting 10 times the amount should take roughly 17 + 8 = 25 years. In the video, they note that it will take 26 years, so we've got a good estimate!

In his Impress by doing compound interest in your head post, Martin Lewis describes the following interest problem: “What is the APR, ie annual interest rate, if you borrowed £80,000 and had to repay £200,000 six years later?”

Since £200,000 ÷ £80,000 = 2.5, we can use a simpler approach than Martin Lewis did in his article, as we know that the rule of 96 with the 6 year time span to work out the annual interest rate. ⁹⁶⁄₆ ≈ 16% interest, the same answer Martin worked out!

USING e: Once you start getting too far beyond 25 time periods (25 years for annual interest rates), you should start using e (roughly 2.71828...) to estimate compound interest over the long term. Last March, I wrote Calculate Powers of e In Your Head! to help with this exact task. At this point, you're probably more concerned with the scale of the answer, rather than the exact answer, so working out just the equivalent power of 10 is all you really need.

SHORT VERSION: So, instead of providing one way to estimating compound interest, here are 3 methods for different scale problems. If the rate is 5% or less, and the interest is applied 5 or fewer time, the binomial method is the way to go. If your problem is larger than that, and covers less than 25 time periods, then use the rules approach (rule of 42, 72, 96, etc.). If the interest is applied more than 25 times, use e to get an idea of the scale.

It may not be the simplest estimation approach for compound interest, but if you're stuck without a calculator, this will help you get by until you can more accurately crunch the numbers.

Money is a tough enough subject on its own. Compound interest seems difficult to wrap your head around, and nearly impossible to calculate without specialized tools.

In this post, however, you'll not only wrap your head around compound interest, but learn some amazing ways to estimate answers quickly in your head!

Compound interest is really all about the time value of money. OK, granted, that sounds like I just switched one buzzword for another. Perhaps having German Nande explain the time value of money in his TED-Ed video will help:



Perhaps figuring out that 10% added to $10,000 is $11,000, but wouldn't it be difficult to work out how long it would take $10,000 to turn into $110,000? Our first tool will begin to make calculations like this easy.

• The Rule of 72: This is one of the most well-known rules in finance. BetterExplained.com has an excellent article on the Rule of 72. In short, if you divide 72 by the interest rate in question, you'll get the number of years it will take your money to double at that interest rate.

For example, for the 10% example in the video, you'd work out 72 ÷ 10 = 7.2, which means it would take about 7.2 years to double your money at 10%. How long would it take at 6%? You work out 72 ÷ 6 = 12, so it would take 12 years to double your money at 6% interest.

To figure out the amount of time it would take to accumulate $110,000 at 10% compound interest, we could think about it in the following manner. In 7.2 years, the $10,000 would double to $20,000. In another 7.2 years (14.4 years total), the $20,000 would become $40,000. Another 7.2 years (21.6 years) would bring $80,000, and a final 7.2 years would take it to $160,000, so we can say that getting to $110,000 would take somewhere between 22 and 29 years.

That's accurate as far as it goes, but can we do better?

• The Rule of 114 and 144: As pointed out over in allfinancialmatters.com, there are similar rules for finding out how long it takes your money to triple and quadruple. For tripling, divide 114 by the interest rate, and for quadrupling, you divide 144 by the interest rate.

Let's see if we can't work out the $110,000 with these new tools. If we could have the original $10,000 triple, then quadruple (or vice-versa) at 10% interest, that would be 12 times our original amount. So, to determine the tripling time, we work out 114 ÷ 10 = 11.4 years. From there, the quadrupling time would be 144 ÷ 10 = 14.4 years. 11.4 + 14.4 = 25.8, or about 26 years. That's the same amount of time in the video!

That's not bad for a mental estimate. There's plenty that can and can't be done with these rules. For example, investopedia points out that using the long term inflation rate of 3%, you can compare prices from years ago to today's prices. At 3%, inflation should double prices every 24 years (72 ÷ 3 = 24), so prices should quadruple every 48 years, and so on.

The caveats explained in MindYourDecisions.com's post on the Rule of 72 should be understood. The rule of 72 doesn't apply when you're getting a variable return (such as stocks and bonds), the interest rate in question is too extreme, or when additional money is regularly added.

That last point is especially interesting. Just how do you calculate interest when regular amounts are included as you go?

• The Rule of 6: Fortunately, MindYourDecisions.com has an answer for that, as well. In that posts example, the author supposed that you add $100/month to an account at 5% interest for 1 year. The calculation shortcut simply involves multiplying the regular deposit amount by the interest rate and the number 6.

The answer given by this estimate is 6 × $100 × 0.05 = 600 × 0.05 = 30. $30 then is the estimate, which is pretty good compared to the actual calculated total of $32.26. If you want to see the accuracy of this formula for yourself, you can play with the numbers involved at this Wolfram|Alpha link. Simply set d to the regular deposit amount (d=100 in this example), and p to the percentage rate (5% is given by p=0.05); Wolfram|Alpha will then return two variables, u, which is the exact amount of dollars in interest you can expect, and v, which is the mental estimate.

Perhaps this rule should be called the rule of half, since you can apply this to any amount of months simply by halving the total number of months involved. How much, for example, could you expect in interest by putting in $150 per month at 4% interest per year, for 5 years (60 months)? We multiply 30 months (half of 60) × $150 per months × 0.04 = $4,500 * 0.04 = $180 in interest. The actual amount, as calculated here, is $181.82, using an additional variable, m, to represent the number of months in question (m=60 for 60 months).

Practice these financial tips, and be ready to astound your friends and family with your financial wizardry!

Scam School has been scammed! Somebody slipped Brain Brushwood some counterfeit coins, and he needs your help to separate the counterfeit coins from the real ones.

OK, this is really just the start of a puzzle, but it's a rather fascinating puzzle. Just when you think you've got the hang of the puzzle, another version can come along and make things tougher.

We'll start by jumping right in to the counterfeit coin puzzles as presented on this week's Scam School (alternative YouTube link):



All in all, not a bad pair of puzzles. For the second puzzle, I would make sure to keep the weighed coins in separate piles, of course, so I can make sure to round up all of the counterfeit coins.

Let's add a new dimension to that second puzzle, just to challenge your thinking. What if, instead of 1 bag holding all counterfeit coins, there were an unknown number of bags? As in the original puzzle, each bag holds either all real coins, each weighing exactly 1 gram, or all counterfeit coins, each weighing 1.1 grams. You still have only one weighing to find out which bags, if any, contain counterfeit coins.

If you want to try and work this out for yourself, stop reading here, as I discuss the solution below.

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If you think about it, what you really need is a series of yes-or-no answers for each bag in a way that allows you to get this information in a single weighing. How do you achieve this?

Our old friend the binary number system comes to the rescue! If you need a quick understanding of binary numbers, watch Binary Numbers in 60 Seconds.

The solution is take 1 coin (2⁰) out of the first bag, 2 coins (2¹) out of the second bag, 4 coins (2²) out of the third bag, and so on. For each bag, you double the number of coins taken from the previous bag, all the way up to 512 (2⁹) coins taken from the 10th bag.

You'll probably note that it's easier to denote the bags as 0 through 9, instead of 1 through 10. With the bags numbered 0 through 9, we can just remember that we take 2^x coins out of bag number x.

How does taking coins out in powers of 2 help? First, consider the weight we'd get if all the coins were real. We'd have 1,023 coins weighing a total of 1,023 grams. Any weight over 1,023 grams, then, can be attributed to the counterfeit coins.

Let's say we try this out, and find that we have a total weight of 1,044.7 grams. Take away the weight of the real coins, and we're left with 21.7 grams extra. At 0.1 grams extra for each of the counterfeit coins, we now know there are 217 counterfeit coins among the 1,023 coins.

That's great, you might say, but we still don't know which bags are counterfeit. If you stop and think for a minute, you may have more information than you think. First, since you took 512 (2⁹) coins out of bag 9, the coins in that bag couldn't be counterfeit. If they were, you'd have a minimum of 512 counterfeit coins in the total.

The same argument could be made for bag 8, from which you removed 256 coins (2⁸). Still, isn't it difficult to work out all the possibilities for the remaining bags?

No, and I can explain why in a very simple way. In our everyday decimal system, how many ways are there to write the number 217? There's only one way, of course, and that's by writing a 2 in the hundreds place, a 1 in the tens place, and 7 in the ones place. The same is true for any other base, include base 2 (binary).

There's only one way to write the binary equivalent of the decimal number 217. To find out what it is, you can either do a binary conversion with the help of a tool such as Wolfram|Alpha, or, if you've been reading Grey Matters long enough, do the conversion in your head.

Done either way, the binary equivalent of 217 is 11011001, but what does this tell us? Each of these numbers represents one of the bags. To be fair and include all 10 bags, we should write it as a 10-digit binary number, 0011011001, and arrange each number under its corresponding bag like this:

9 8 7 6 5 4 3 2 1 0
0 0 1 1 0 1 1 0 0 1

It's time for some magic!

Don't worry, there's no complicated sleight-of-hand in these tricks. Not only does math make them easy, but you don't even have to do any math during the routines, since all the math involved has been worked out ahead of time.

I'll start with the simpler of the tricks. In this first one, you have someone think of any hour of the day, and you tap numbers on an analog watch while they silently count up to 20. When they reach 20, they say “Stop!”, and your finger is on the hour they secretly chose!

The method behind this simple trick is described in Futility Closet's On Time post.

At first, the workings may confuse you, but a little experimentation with different numbers will help you understand it. Obviously, this is also true for anyone for whom you perform it, so don't treat this as a big mystery, but rather as a simple and interesting experience.

The basic tapping presentation has a long history in magic. In Martin Gardner's book, Mathematics, Magic and Mystery, there's an entire section on tapping tricks. Thank to Google Books, you can read the entire section online for free, running from page 101 to page 107.

The next trick, courtesy of Card Colm, is a little more involved. You have someone name any card suit, have a regular deck of cards shuffled, and then the number cards (Ace through 9) are removed in the order in which they're found in the deck. You then make an unusual bet based on divisibility of various numbers formed by those cards.

This trick is called the $36 Gamble, and the method is found in Card Colm's post, The Sequence I Desire. Magic: When Divided, No Remainder. Beyond just the mathematical method, there's plenty to explore under the hood of this routine, including Arthur Benjamin's method for determining divisibility by 7, and a very deceptive shuffling method, which appears fair.

If you enjoy the deceptive shuffles discussed in the above post and its links, you also might enjoy Lew Brooks' book Stack Attack, which features the False False Shuffle. The false shuffle and the routines in Stack Attack mix well with the principles behind the $36 Gamble. In my 2006 review of the DVD of the same name by the same author, you can get a better idea of the contents.

Even though I've only linked to 2 tricks here, practicing them, understanding them, and digging in to the variations I've mentioned is more than enough to get your mental gears turning, so have fun exploring them!

(Note: This is a repost, with some link updating and minor rewriting, from about this same time 5 years ago. I repost it because it has become relevant over this Memorial Day weekend.)

If you do math at all at the gas pump, it's probably either related to how many gallons you can get for a given amount of money, or how much money will be required to get a needed amount of gas. If you're willing to do a bit of math and planning before you go get your gas, you can actually work a surprising amount of real savings into the equation, as well.

How do you save on gas? The obvious first answer is to find the cheapest gas you can. My grandfather's method for this was to drive around looking station by station, but that only works well when you're sure you can find gas lower than 35 cents/gallon. Unsurprisingly, the internet is here to help! Sites such as fueleconomy.gov, FuelMeUp, and GasBuddy make short work of finding the lowest gas prices in your area.

Unless you find the cheapest gas in your immediate area, another question begins to raise its head at this point. Sure, if you go a little farther to that station with the cheap gas you can save some money, but if you factor in the gas you'll burn going the extra distance, and the added gas you'll require, are you really saving money? With the current level of gas prices, this isn't a trivial question.

Fortunately, Kimberly Crandell, better known as Science Mom, tackled the question of whether nearby expensive gas or cheaper gas across town was cheaper in July 2007.

As I've explained, there is some math involved, but there are only five different factors involved: The number of gallons needed, the gas mileage of the car, the cost of the closer (more expensive) gas, the cost of the farther (cheaper) gas, and the miles out of the way for the cheaper gas (Google Maps, Yahoo! Maps, or MapQuest will come in handy here). In the article, you learn the formulas to process this, and how to solve for the savings you'll get, as well as the break even points for cost per gallon, total gas gallons, and distance.

Understanding and working through the formulas is one thing, but how about if you would just like to get your answer and go? Once again, the internet is here to help. My favorite tool for this step is Instacalc, which I first mentioned in August 2007.

I've created an instacalc version of Kimberly Crandell's equations where all you have to do is plug in the five factors (remembering that the two prices requested are both price per gallon).

If you prefer, I've also created a metric version of this calculator, for readers in other countries. Whichever version you use, I hope this helps save you some money and that you find it useful!

Update: If you enjoy William Spaniel's Game Theory 101 videos, you'll enjoy his method of finding cheap gas without perfect information. This method, based on game theory, is equally mathematical, but requires fewer calculations.

My regular readers might be looking at the title and picture and wondering whether they're on the right blog. I normally post about doing math and memory in your head, not on a calculator.

However, using your brain in conjunction with a simple 4-function calculator, you can get much more out of them than you may have ever thought possible.

Since you only see functions for addition, subtraction, division, and multiplication (and sometimes a square root function) on a 4-function calculator, most people limit their use to just those few functions. However, even a simple pocket calculator has a few hidden features that, when combined with an understanding of varous aspects of math, allows you get much more out of it.

Before you try these out, make sure you're using an actual 4-function calculator, as more complicated calculators act differently. Many calculator apps on mobile devices appears to be 4-function calculators in one orientation, and scientific calculators in another orientation. Unless you discover for yourself otherwise, these calculator apps are generally always working as a scientific calculator, even when it appears otherwise.

Over at Ted's Math World, there's a very complete course in using a 4-function calculator, which includes these sections:

1: Introduction to Programming a Four-Function Calculator

2: Integer Powers

3: Integer Roots

4: Trigonometry

5: Compound Interest

6: Logarithms

7: Extra Decimals for Square Roots

8: Some Arithmetic Shortcuts

Even if you don't go through every section, at least go through the introduction section, as you may learn about some hidden features of your pocket calculator. Ted's Math World also features a very simple continued fraction approach to square roots, and in the Integer Roots section, you can learn how to enter this into your calculator.

Eddie's Math and Calculator Blog also has a course on calculator usage called Calculator Tricks. Surprisingly, there is very little crossover with the above course, and this one gets as far as dealing with 2 by 2 matrices! Eddie's course is available at these links: Part 1, Part 2, Part 3, Part 4, Part 5.

Back in 1974, when 4-function calculators were just starting to become affordable and popular, Popular Science wrote up an excellent guide, including many common real-word uses, such as photography, cooking, and shopping. True, you might have apps on your mobile device that handle similar functions today, but it's still good to know how to handle them yourself. The article, titled New Tricks For Pocket Calculators, can be found in the December 1974 issue of Popular Science, on page 96, page 97, page 98, page 118, and page 119.

Go through these resources, and you'll start to get a good idea of just how much more powerful your 4-function calculator can truly be!

Don't forget to keep an eye out for the occasional individual tips, as well. For example, here's a quick way to find any root on a 4-function calculator, as long as you have a square root button available:



One kind of math that doesn't get much coverage on calculators is modular arithmetic. If you're not familiar with modular arithmetic, BetterExplained.com and Martin Gardner (page 1, page 2) have excellent introductions.

Surprisingly, even many models of scientific calculators don't have basic modulo functions. In the few places I have seen methods for working out the modulus on a calculator, the methods were similar to the ones taught in this xkcd.com forum thread.

That method is certainly useful, but I never cared for the back-and-forth nature of it. I developed another method (other people must have come across this, but I've never found a reference to it) which takes you straight to the answer. Let's say you're trying to figure out what 83 mod 13 equals. Simply enter 83 - 13 = on the calculator, and you'll see 70. Hit equals again, and you see it drop down again to 57. Keep hitting the equals button until you come to a positive number that is less than 13, and that's your answer! In this case, the answer is 5.

For any number x mod y, just start with by entering x - y =, and then keep hitting the equals button until you wind up with a non-negative number that's less (LESS - not LESS THAN OR EQUAL TO) than y, and that's the final answer.

This answer works well when the numbers are relatively close, or at least have the same number of digits. What happens, though, if you have to work out something like 96,528 mod 17?!? In this case, we use powers of 10 to help. What number starts with 17, ends in 1 or more 0s, and is less than 96,528? It's easy to see that 17,000 fits the bill, so we start with 96,528 - 17,000 =, and keep hitting the equals button until we get a non-negative number that is less than 17,000. After this, we wind up with 11,528. Now, drop a zero from 17,000 to get 1,700, and repeat the process starting with 11,528 - 1,700 =, resulting in 1,328. Repeating this with 170, we work our way down to 138. Finally, we go through this process one last time with 17, and we come to our final answer, which is 2.

So, when working through any modular problem, you can not only take the number itself out, but add an appropriate number of zeroes to the end, and them out by the hundreds, thousands, millions, or whatever scale is needed! This approach may take longer, but it goes to the answer directly, and helps you understand the process of modular arithmetic.

You can also use a similar process with addition in order to find congruent numbers. What numbers are congruent to 2 modulo 6? Start with 2 + 6 =, and you'll get 8. Hit equals again, and you should get 14, then 20, and so on. Each of the displayed results are numbers that are congruent to 2 modulo 6: 2, 8, 14, 20, 26, 32, etc.!

Give a little thought, a little fun, and a little effort to your simple 4-function calculator, and you just may be surprised by what you can do with it!

When it comes to age guessing, very few people think of the calculator feats such as the one in the previous post.

The first thing that usually comes to mind is carnival age-guessers. In this post, we'll take a closer look at age-guessing as a skill.

The best tips I've found on determining someone's age are in the article How to Guess Ages More Accurately. Since men tend to put less effort into hiding their age than women, here are a few extra tips on guessing a man's age.

Just knowing these tips isn't of much good without practice. Thankfully, there are several sites where you can practice guessing the age of random people:

• How Old Are You?
• Guess my Age
• Match>Age

Even though carnival age-guessers aren't having you put any numbers in a calculator, they're still able to use some very subtle math tricks. For example, instead of advertising that they'll hit your exact age, you'll usually see a margin of error such as, “I'll guess your age within 3 years!” That sounds quite close to most people.

If you think about it, however, a 3-year margin of error really isn't that close. If someone is 35, a guess of anywhere from 32 to 38 would be considered correct. In other words, all they have to do is be within the decade you were born in, and they'll be considered correct. The more experience they have, the smaller margin of error they can offer. For example, professional age-guesser Lee Bennett used an impressive 1 year margin of error.

Even more central to an age-guesser's actual purpose is the simple economics of the situation. Let's assume that the cost to have the carny make a guess is $3, and the cost per stuffed animal to the carnival is $.25 (since they buy them in bulk). If we assume the guess is wrong every time, perhaps to keep every customer flattered, they're making an 1100% profit on each prize!

As the guesser becomes more skillful, the profit margin goes up! If we assume the age-guesser can correctly guess the ages of 4 out of 5 people (an 80% success rate), then that's 5 people times $3/person or $15 they're taking in. Only 1 wrong guess out of those 5 means that they're giving up $.25 for every $15 they take in, a staggering 5900% profit margin!

So, when it comes down to it, age-guessing as a skill is all about the margin of error and the profit margin. And that's assuming they don't employ standard scams like writing two ages and then covering up the one that's farther away, using magician's techniques to write down a close answer after you state your age, or simply pickpocketing your wallet and looking at your ID.

Guessing ages is a skill, but only ever an approximate one at best. The mathematical approaches, as we've seen, offer precision. Perhaps the best approach is to develop the skill of age-guessing, and use math in a way that doesn't detract from the skill.

That's the approach we'll start developing in the next post in this series.

(Note: This is a repost, with some link updating and minor rewriting, from this same week 3 years ago. I repost it because it has become relevant again.)

If you do math at all at the gas pump, it's probably either related to how many gallons you can get for a given amount of money, or how much money will be required to get a needed amount of gas. If you're willing to do a bit of math and planning before you go get your gas, you can actually work a surprising amount of real savings into the equation, as well.

How do you save on gas? The obvious first answer is to find the cheapest gas you can. My grandfather's method for this was to drive around looking station by station, but that only works well when you're sure you can find gas lower than 35 cents/gallon. Unsurprisingly, the internet is here to help! Sites such as fueleconomy.gov, FuelMeUp, and GasBuddy make short work of finding the lowest gas prices in your area.

Unless you find the cheapest gas in your immediate area, another question begins to raise its head at this point. Sure, if you go a little farther to that station with the cheap gas you can save some money, but if you factor in the gas you'll burn going the extra distance, and the added gas you'll require, are you really saving money? With the current level of gas prices, this isn't a trivial question.

Fortunately, Kimberly Crandell, better known as Science Mom, tackled the question of whether nearby expensive gas or cheaper gas across town was cheaper in July 2007.

As I've explained, there is some math involved, but there are only five different factors involved: The number of gallons needed, the gas mileage of the car, the cost of the closer (more expensive) gas, the cost of the farther (cheaper) gas, and the miles out of the way for the cheaper gas (Google Maps, Yahoo! Maps, or MapQuest will come in handy here). In the article, you learn the formulas to process this, and how to solve for the savings you'll get, as well as the break even points for cost per gallon, total gas gallons, and distance.

Understanding and working through the formulas is one thing, but how about if you would just like to get your answer and go? Once again, the internet is here to help. My favorite tool for this step is Instacalc, which I first mentioned in August 2007.

I've created an instacalc version of Kimberly Crandell's equations where all you have to do is plug in the five factors (remembering that the two prices requested are both price per gallon).

Great minds think alike! I recently added a new section of Penny Puzzles to the Grey Matters Store. A little over 1 week later, Scam School covers the same puzzle!

Before I get to the Scam School episode itself, let's cover the basic challenge first.

Start by drawing a 5-pointed star, and then place a penny (or button, or other small object) on one of the points, and slide it along either connecting line to another point. That's not hard so far, right?

Next, put another penny on any empty star point, and slide it along a line to any other empty star point. The challenge is to place 4 pennies on the star in this manner.

Before you try it, it seems easy. Most people find that they can only get to 3 coins, and find the 4-coin solution unusually elusive.

Let's change the puzzle a bit, but keep the rules the same. Here's an online version that uses an 8-pointed star (Java required). The rules are the same, but you're trying to place 7 pennies this time. Try playing this version without using the hint button and/or the explanation link as long as you can.

Perhaps there's something tricky about those lines? Let's try a similat 9-dot challenge, but just with counting (Flash required), both clockwise and counter-clockwise. The object this time is to turn 8 dots white.

Isn't it maddening that such a seemingly simple task should prove so elusive? As a solo game, this can provide hours of puzzlement.

Leave it to none other than Chico Marx to turn this into a hustle with money. Thankfully, Scam School shows you not only how Chico Marx turned this into a bar scam, but also how to beat this maddening puzzle:



The method taught here is taught so well, it shouldn't take long to work how it applies to all the other versions, as well.

Obviously, if you're doing the Scam School version above, you should go last, as suggested. However, if you're just challenging a friend or two to solve the puzzle, you'll find that if you can demonstrate the solution without explaining the method behind it, your friends will still have trouble solving the puzzle!

Try these out for yourself, and let me know in the comments of anything interesting that happened when you played this yourself, or challenged your friends.

Learning about how scams work can be a fun gateway to learning surprising things about math and psychology. But what about when you're on the go? Get out your Android and Apple iOS mobile devices for this post!

Disclaimer: As with any column on scams on Grey Matters, I don't condone using these to rip people off, and simply present the information about scams here as an educational tool. Proceed with this in mind, and at your own risk.

Before we even get to apps, don't overlook the built-in features of your mobile device(s).

With the ability to view video on YouTube and/or subscribe to podcasts, you can check out programs such as Scam School (Scam School homepage), The Real Hustler UK, The Real Hustle US, and more!

The ability to surf the internet, as always, can also bring a wealth of information. Besides learning about scams here on Grey Matters, searching around forums can be excellent resources. There's the Scam School forums, as well as the various Magic Cafe's great forums, including The Gambling Spot, Pardon me, sir..., If right you win, if wrong you lose..., Betchas, Magical equations, and Puzzle me this....

A good blog to check out is Australia's Honest Con Man: Confessions, and his previous archives at The Honest Con Man's Guide To Life.

One of the most popular mathematical scams is the game of Nim. It has already made 4 appearances on Scam School (Nim, Advanced Nim, Thirty-One, Calendar Nim).

Watching those videos is one thing, but why not use your mobile device to practice and learn more about it? It's not surprising that Nim is so readily available for mobile devices. In the early days of personal computers, it was already popular. There were basic versions, such as 23 Matches, Batnum, and Nim. Some of the versions, such as the amazing Android Nim for the PET and TRS-80, did an amazing job of presenting this classic game!

On the Android you can get NimDroid and NimSwitch, both available for free!

For iPhone/iPod Touch and even iPad users (using the iPad's "2x" mode for these apps), there's plenty of free Nim versions, including myQuickGame Free, NeonNim: The Subtraction Game, Nim Game, and PYMINIM. Update: (August 17, 2010) Another Nim game, the Race To 100 app, was originally released for 99 cents, but has been free since August 8th. This is the version of Nim taught in the 116th episode of Scam School.

If you're willing to spend a little money, there's also some nice commercial versions of Nim for Apple's mobile devices. Dual Matches, Mind Nimmer, myQuickGame, and Nim.

Special mention should be made of the commercial Cannibal Muffin and Last Stone apps. Like the aforementioned 1970s Android Nim, the authors have taken extra time and care to present Nim in an extraordinary way.

Getting away from Nim, what about this interesting problem, known as the Monty Hall Problem?



Scam School also covered this, explaining how this fooled over 1,000 PhDs when it was discussed in Marilyn Vos Savant's column. Apple mobile device users use can try this counter-intuitive problem via the commercial Monty Doors or the free Monty Hall Paradox apps.

Although you can't win with this scam every time, you can win often enough that there are con men out there who use the Monty Hall Problem's counter-intuitive nature to their advantage.

While Nim and Monty Hall reign as scams from which you can learn great lessons, there are many other ways to learn about scams with your mobile device. For iPhones, iPod Touches, and iPads, Bar Tricks Free teaches you some basic scams, and its big brothers, Bar Tricks I and Bar Tricks II, both of which are paid apps, can teach you more. iDrink4Free and Gags are also available on the App Store.

Update: (August 17, 2010) The Author of the previously-mentioned Race To 100 app, also has another app called FourQuarters. From what I can tell, it's a version of the four-coin puzzle taught on the 2nd episode of Scam School.

If you're really serious about understand why these and similar scams work, Bruce Frey's book Statistics Hacks (also available in paperback) is a great, clear way to understand these often perplexing propositions. You can get a free preview of this book here, as well as the paperback link.

I'd love to hear about any insights you've developed by playing with these apps. Also, if you have any others that are relevant, I'd love to hear about them. Talk to me in the comments!

I've posted several times before on game theory, but I keep finding more and more interesting game theory works on the web.

My favorite game theory resource, Mind Your Decisions, teaches how to find cheap gas using game theory. When you have perfect information about gas rates, it's a simple matter of running the numbers through the right equations. However, the Mind Your Decisions article teaches a surprising way to find a good price without knowing the prices of all the local gas stations!

The gas approach was brought up by William Spaniel, whose excellent lectures on game theory are available on YouTube. Subscribe to JimBobJenkins' channel to get new ones as they become available. With the exception of the Terramorphic Expanse video (see video note), which was purposely posted out of order, the videos should be watched in the order they were posted.

Benjamin Polak's free Yale game theory course, which I mentioned last November, is still a good (and free!) course, as well.

Getting back to the Mind Your Decisions post about gas and cars, Bruce Bueno de Mesquita has used his game theory expertise to develop a car-buying approach that gives the advantage to you, instead of the car dealer. TED fans will recognize Bruce from his analysis of Iran's future.

For something called game theory, we sure haven't talked much about games as most people think of them, have we?

On very popular game is the popular Deal Or No Deal game show. Unlike many game shows, this one boils down to almost pure mathematics, and can be played as such. Game theory is well-suited to analyzing your best moves at any point in the game, as discussed in this chapter of Introduction to Game Theory. In Deal or No Deal: A Statistical Deal, an effective strategy is even developed and explained.

Once you read that strategy, you might wish you could try it out yourself. If your browser still supports Flash, you can play the official NBC online game. If you're on an iPhone or iPod Touch, you can play the free web app version in your browser, or buy the official native app.

As always, I hope you find these links fun, useful, and perhaps even educational.

Some problem remain unsolved because they're simply so challenging. Other mysteries remain unsolved simply because they haven't bugged enough people that someone finally sits down and solves the problem. Today, we'll take a look at some interesting mysteries that have finally been solved.

Want some money? I've got a game that will guarantee you money! I have 2 envelopes that both contain money, but 1 of the envelopes contains twice as much money as the other one. You only get to keep the contents of 1 envelope, but you do get to make a choice. Just to make in more interesting, I'll let you choose either envelope, check to see how much money is inside, and then decide if you want to switch or not. If you don't switch, you keep the money in that first chosen enevelope. If you do switch, you keep the money in that 2nd envelope.

At first, this sounds like a simple variation of the Monty Hall Dilemma, but there's an important difference. In the Monty Hall Dilemma, you know the hidden contents (2 goats, 1 car). In this two-envelope challenge, you start with no knowledge of the exact contents, and then gain a partial knowledge.

The long run of this challenge has always been how to maximize your return. You could just always switch, and you'd get the larger envelope half of the time. The same thing would happen if you never switched. Yet the calculation of expected return suggests you should always switch. Earlier this year, a group of researchers from Australia actually worked out a surprisingly simple strategy for maximizing your returns in this two-envelope paradox.

Either way, you've got your money, let's go get some pizza with it! On Grey Matters, I've actually discussed pizza quite a bit, from the Pizza Theorem to using geometry in a pizza parlor to save money. Here's another challenge: How do you fairly divide a pizza?

If pizza places always divided their pizzas into exactly equal slices and always cut exactly through the center, this would be a relatively simple problem. However, whenever you get a pizza in the real world, some pieces are larger, some are smaller, and the cut isn't always through the exact center. As Yogi Berra once said, "In theory, there's no difference between theory and practice. In practice, there is."

Under these conditions, how do you divide up the pizza fairly? It would be especially handy if there were no calculations, so that the pizza doesn't get cold while you work out the answer.

The answer to this problem was found, not surprisingly, by a group of mathematics students who enjoyed hanging out in their favorite pizzeria. Study the answer well, as many pizzas were left cold in pursuit of this important information.

One mystery that got plenty of attention this week was a mysterious spiral in the sky over Norway. It appeared as a white spiral with a blue streak shooting out of the middle. The mystery was solved when it was discovered that it was a misfiring rocket launched from Russia. The video here shows how the spiral and streak occured, along with some stunning photographs of how it actually appeared.

There are still plenty of unsolved math-related problems, but have you ever noticed that the closer a problem is to our immediate interests, the more quickly it gets solved? Even the backers of the Millennium Prize realize this, which is why they attach a $1 million prize to these unsolved problems.

Dealing with memory and living in Las Vegas, I suppose it's inevitable that I should get around to discussing how to memorize basic blackjack strategy.

Before anything else, make sure you understand the basic rules of blackjack. If you don't get the basic rules down first, nothing else will help. Beyond just understanding the fundamental rules, you should also be aware of the rules imposed by particular casinos, and read up on the different variations when possible. For example, are those single deck blackjack games that pay 6:5 on a blackjack a good deal?

Once you understand the rules, you need to be able to learn to play effectively. This is where basic strategy comes in. Basic strategy is most familiar to people as those little blackjack charts like this. Above and beyond the strategy cards, I've even developed basic blackjack strategy T-shirts (note that the charts are printed upside-down, so you can read them while wearing them) as one solution, but it's really better to memorize them if you can.

Disclaimer: Before we continue on, remember that no method of playing can guarantee you win, which is why it's called gambling. In this article, I'm merely focusing on the challenge of memorizing basic blackjack strategy. This should not be taken as an endorsement or encouragement of gambling, and Grey Matters can in no way be responsible for any wins, losses or other consequences (including damages) that happen as a result of following the advice in this blog.

When memorizing a chart, you might think that the best approach would be to take an approach that's similar to my 400 Digits of Pi feat. However, doing blackjack strategy this way is actually twice as difficult, as there would 230 spots to memorize on such as chart.

The first rule when memorizing something is to minimize what you need to remember later. Thankfully, due to the large ranges of similar strategies in basic strategy, this is possible. The best work I've seen on minimizing basic strategy rules is in an iPhone/iPod Touch native app called Easy Blackjack Cheat Sheet (EBCS - iTunes Link), which breaks the entire chart down into 17 simple rules to remember, and it's available for free!

To give you an example, the whole approach boils down to the 4-line rhyme: SURRENDER, SPLIT, DOUBLE, HIT. In other words, you first ask yourself whether you should surrender or not, then whether to split or not, followed by whether to double or not, and finally whether to hit or not, and always in that order. For each of these rules, simple mnemonics are provided to remind you when you should take each of those actions, as well as when to ignore the decisions. For example, in the second screenshot here, you can already see that you don't think about splitting if you don't have a pair, and that the time to split 2s, 3s and 7s is only when the dealer has a 2 thru 7 showing. “2s, 3s, and 7s vs. a 2 thru 7” is pretty easy to remember.

EBCS is only a method of helping you memorize the correct play for various hands. If you're serious about memorizing basic strategy, you need to practice it during actual play, too. I've found that PepperDogSoft's Blackjack Teacher works well for this, and there are many other native apps available, as well. Instead of playing a full game, it only focuses on the initial deal and the proper choices to make. It also tracks your streaks of correct answers, and even reminds you of the length of your longest correct answer streak. Before EBCS, I had trouble getting a streak of just 3 correct answers going, but now streaks of 10 or more weren't difficult to reach less than a day after getting it.

As long you're practicing with an iPhone/iPod Touch anyway, probably the most effective approach would be to learn and practice as above. However, when you're going into a real casino game, make sure you're aware of the rules at the particular casino of your choice (the chart at that link is for Vegas only), and then use the basic strategy engine at Blackjack.info to find the best plays for that game. Usually, there are only a few plays that are different, so making up 1-3 of your own mnemonics to adjust the rules is all that's required and will be time well spent.

On Monday, Apple amazed many of it's fans at the WWDC 2009 Keynote, including new announcements about Safari 4, Snow Leopard, the new MacBook Pro lineup and the new iPhone 3G S. Even if you're not working for Apple, you too can still use the iPhone or iPod Touch to amaze people yourself.

The iPhone Flashcard Apps I recently listed should not be forgotten here. The trained memory you develop with these can be used in many ways to amaze people, such as in a memory demonstration or as the secret to a magic effect.

If you hadn't noticed yet, there are already a good selection of iPhone- and iPod Touch-based magic effects.

Mind Reading

• Age Square (Free WebApp Zip Archive!): In this effect, you show a magic square, and ask if the person sees their age in the magic square. They then go through 4 screens, each one with several squares highlighted, and asking whether the person sees their age among those highlighted squares. At the end, another magic square is shown, and it adds up to the person's age in every direction! The program will even optionally step through the numerous arrangements that add to their age.

Werner Miller created this effect especially for Grey Matters. There is now a video tutorial for Age Square available on YouTube. If you'd like to try it out, you can try it out here, but if you're going to do this on any kind of regular basis, please download the file archive, unZIP it, and upload it on your own server space!

• Epicore iPhone Magic (iTunes Link): Rather than a single program, Epicore is an iPhone development company that has a very strong selection of magic routines for the iPhone. From reviews by fellow magicians, their magic app developers think deeper about their magic, and the routines are far more deceptive as a result. Their routines include MindCard (iTunes Link), iDetect (iTunes Link), iCoinPredict (iTunes Link), iCardPredict (iTunes Link), DestinyCard (iTunes Link) and FaceCard (iTunes Link). Faria, from Magiclaffs.org, who first told me about Epicore's magic apps, has a handy tip for those who buy and perform FaceCard: To let your audience member have the resulting picture as a souvenir, press the home and power buttons at the same time to take a snapshot of the screen, add your contact information onto the photo automatically using Imangi Studios' PhotoMarkr app (iTunes Link), and send it to the spectator's e-mail address!

• Google App: In this routine, you have a spectator name any playing card, and then have them ask Google what their card is. Real Google search results are returned, each containing the name of their playing card!

• iForce (iTunes link): Through an interesting use of the iPhone's capabilities, you can apparently predict the outcome of an amazing array of choices. It's disguised as a drawing program, which is also available in the iTunes store. The whole idea is very well thought out. To get a better idea of what it does, watch the videos at the iForce link above.

• iKnow: You show someone your playlist of favorites, and have them choose one song randomly off this list, listen to it, and then imagine the song they heard. You then listen in their ear, as if you're trying to hear what remains of the rhythm in their head, and then name the chosen song! This effect isn't limited to just the iPhone and iPod Touch. It will work with just about any MP3 player out there!

• iMagic: In this iPhone card routine, you have several spectators name a card by having one choose number or picture cards, one choose a suit, and the final one choose the number. Without touching the iPhone, the named card appears briefly over the iPhone menu, and then vanishes. The hands-off handling of the iPhone, along with the card being named instead of chosen, add to the seeming impossibility.

• iSensor (iTunes link): In this effect, you show a screen with 5 ESP symbols (star, cross, wavy lines, circle and square), turn the phone face down, and ask them to name anyone of the symbols. You then pick it up and show that it is the only symbol remaining on the screen! If they think this is simply done with Voice Control, you can repeat the effect, and have them make their choice known by drawing the symbol in the air. I first mentioned this one back in May, but it deserves mention here, too. There are effects with a similar principle, such as iMystical and iThought Receiver, but iSensor comes across as the most mystifying and deceptive.

• MagiCard (iTunes link): In this effect, a card is chosen from a real deck, and the image of the selected card appears on the iPhone, all without the performer ever touching the iPhone! As you can see from the videos, there are actually multiple ways you can present this effect. The hands-off nature of this routine makes it very deceptive.

• MindBeam: In this video, you beam an app to another persons iPhone. The App displays 3 playing cards or postcards, and they secretly choose one while you're out of the room. When they call you back in, you can name their selection! Performed properly, this can be an amazing piece.

• Mobile Opener: This effect is a professional stage magic routine that isn't limited specifically to the iPhone and iPod Touch, but members of your audience can use their iPhones to take part in it. In the routine, numbers given by the audience are then totaled. The total is then shown to have been predicted. It sounds simple, but the real strong point is the presentation, which is intended to generate audience interest at the beginning, and work the next speaker or the client's product/message into the effect.

• Pick Any Card (iTunes Link): A face card is on the face of the iPhone/iPod Touch, and a spectator is asked to guess whether this card is red or black, and their guess is shown to be correct. Next, the performer asks the spectator whether they think a face down card is high or low, and the spectator's guess proves correct again! Since the spectator seems in tune enough, they're asked to name any card, and then to flip the card over on the screen. Think you've got this one figured out? If so, consider the fact that at no point in the routine does the performer ever touch the screen!


Production Effects

There are numerous production effects in which you appear to remove an object from the screen. They all have the same basic method, but in the right time and place, these can be amazing interludes. Among the objects you can produce from your iPhone are cards, bills (comedy version), coins (including slot winnings!), popcorn, matches and sponge balls.


Other
Here are the works of those venturesome soles who like to create magic that doesn't fit neatly into pre-determined categories.

• Books: If you look, there are many books of magic effects that have many routines that can be adapted to the iPhone or the iPod Touch with a little thought. If you're going this route, my first two must-have recommendations are Impuzzibilities and Further Impuzzibilities by Jim Steinmeyer. These two works not only teach original effects, but are excellent object lessons in how to disguise mathematical and other self-working principles. From there, good sources of inspiration can be found in Karl Fulves' Self-Working series of books, such as Self-Working Number Magic and Self-Working Mental Magic.

• Easy iPod Magic: This magic.about.com page has 2 free tricks, The Animated iPod Man, in which your iPod seems to bring a paper-drawn stick figure to life, and The iPod Card Trick, in which the iPod makes the name of a selected card appear in a square drawn on paper. The former is cute, and the latter seems to be the same, until the iPod is removed, and the real drawing has changed. The screen ratio of the included videos are intended for classic iPods, but the idea could easily be adapted for the iPhone and iPod Touch. Even if you don't have the skills or software to create a video, a sequence of picture in the photo album could be used to make the picture appear.

• Magic Compass (iTunes link): Simply put, you can place any object anywhere around the iPhone, and the Magic Compass will point right to it. With the iPhone 3G S' new compass feature, this effect is actually quite relevant. The same site also offers a cuter version of the same trick with bunnies (iTunes link).

• iPunk'd: You definitely won't find this one on the App Store, as there's nothing to download! In iPunk'd, you take someone's ear phone cord, and cut it with scissors. Before they kill you for destroying their headphones, you magically restore the cord! Yes, this is the cut & restored rope updated and made relevant. If you're familiar with how to use a certain silk-vanishing gimmick to cut and restore a rope, that would make this routine even more deceptive.

• iScan: This one isn't quite a mind reading effect, and it isn't quite a production, so it wouldn't fit in the first 2 categories. In iScan, a card is selected from a deck, returned, and shuffled. You then use your iPhone to scan the spectator. You then run your hand back and forth underneath the iPhone's camera, and the image of the card appears on your hand. Here's a YouTube video of the effect being performed, so that you can get a better idea of this strange effect.

• iUtility: This is from the makers of the Magic With the iPhone DVD below, but instead of having the tricks happen on the iPhone/iPod Touch, this DVD focuses on using the use of your handheld as the method behind tricks, such as switches or vanishes.

• Magic Tattoo (iTunes link): A number is chosen, and used to find out which ESP symbol corresponds with that number. That symbol is then dragged onto a picture of a hand, where it appears on the palm. When you lift the iPhone off of your hand, that same symbol is on your real palm!

• Magic With the iPhone DVD: Nicholas Byrd has put out a 2-disc set of iPhone magic. The first is a performance and instructional DVD, while the other is a data disc, containing all the files needed to perform the effects. Among the more standard iPhone magic effects, such as producing money and the princess card trick (which was overdone on the web long before the iPhone came along), there are more intriguing uses, such as a Hot Rod routine, a penny-to-dime effect, a prediction effect with the icons themselves, and more! The Unofficial Apple Weblog has a review of it here. Not enough for you? You'll be glad to know there's a 2nd volume available now, as well as iUtility (above).

• Predictext (From Mind Blasters): In this routine, you text a message to someone in the audience, and then have them shuffle, cut and deal half of the deck, as you do the same with the other half. You ask if it would be amazing if both sets of dealt cards would have all matching pairs on top (such as both red 10s, both black 5s and so on). Unfortunately, it doesn't work out. However, the top cards on the spectator's pile is correctly predicted on the text message sent earlier! This is probably a rather strange entry for this list, as it depends on a feature most cell phones have, but isn't readily available on the iPhone – SMS Templates. However, there are 3rd party apps which can offer this feature (even for the iPod Touch through AIM!). The routine could also be reworked with AlibiSMS (below), but as you ultimately want your contact information left on a spectator's cellphone, I wouldn't go this route.

• Spirit Photo: This effect seems to dance on the border between prank and magic effect. You borrow a spectator's iPhone, mentioning that you're going to install a “Spectral Filter” for the iPhone camera that can photograph dead spirits. Once the filter is installed, you mention that it works best with pictures of dead people, so you ask them to take out a bill of any denomination. You snap a picture of their bill, but when they look at it, the skull of the person on the bill appears on it! It really is in their photo album, and they can keep it or delete it as they wish.


Not Magic, But . . .

• AlibiSMS (iTunes link): This is a fun app that lets you enter a text message that can be scheduled to come up on your phone later, as if it were happening at that time. With a little creative thinking, this could be used to reveal a prediction.

• Banner (iTunes link): This could be an interesting way to reveal a prediction. It's appears to be an array of LED lights, across which a message scrolls. Here in Vegas, sending a message that way can be very thematic. In a similar vein there's Light Writer (iTunes link), which is basically an iPhone version of those SkyLiner novelties (although since the SkyLiner is only $20/unit, I think I'd rather risk dropping one of those than an iPhone or iPod Touch).

• Deckster (iTunes link): This isn't quite a magic effect, but rather a playing card deck simulator. This App goes to great length to simulate the experience of a deck of cards, down to the opening of a new deck (you even have to remove the seal!), dealing and shuffling the deck in numerous ways (overhand, riffle shuffle and more). The web page hints you may even be able to deal seconds and bottoms, but they're not saying exactly how. This is just too creative not to share here.

• Magic Café's App Forums: The Magic Café now has 3 forums dedicated specifically to magic apps: APPS-alutely (for general discussion of apps), APPealing or APPalling? (for app reviews), and APPearing Soon... (for discusing app announcements, rumors, and marketing). This is a great way to keep up with the latest magic apps.

• Mathemagics (iTunes link): This program gives you lessons on how to quickly solve several challenging arithmetic problems in your head, and then lets you practice your newfound skills. Lightning calcuator-style feats are not only amazing in and of themselves, but are also useful as a build-up to seemingly more difficult feats, such as mind-reading.

• QuickCal (iTunes Link): Do you perform the Day of the Week for Any Date feat? If so, this calendar app is the perfect way to demonstrate that you're correct. Just select the year via the spinning-wheel picker, and you can see a single month, 2 months, 4 months, 6 months, or even a whole year at a glance. True, you could use a perpetual calendar web app, but QuickCal is great for when you don't have a Wi-Fi connection.