Since I released Day One, my approach to the classic day of the week for any date feat, I've been hearing back from people who've bought it.

Some of them have developed some ingenious handlings for it that they've graciously allowed me to pass on to you.

Because Day One is a commercial product (more info available here) I am going to have to be intentionally vague about some aspects of the method. If you own the routine, however, everything should be clear enough.

The first tip involves the use of Wolfram|Alpha. Before you even ask for a year, ask your audience if anyone is carrying a mobile device on them that is currently able to access the internet, and to take it out and turn it if they do. You tell them to access wolframalpha.com, or use the Wolfram|Alpha mobile app, if they have it.

Once everyone with an online mobile device is ready, ask for the year. When the year is given, mention to those people online that they should type in the year followed by the word calendar. For example, if the year called is 1978, you tell your audience to enter the phrase 1978 calendar and hit return (or click the little orange equals sign).

At this point, you'll have a natural pause while people type, which allows you some extra time to determine the doomsday for the given year. Once you get the year's doomsday, you can ask, "Does everyone have a calendar before them? Good!"

This also help minimize the need to carry a perpetual calendar for verification. Be aware that mobile devices may not always be present or may not have online access, so there's still a need to carry a perpetual calendar. You can find an offline perpetual app for your system using Quixey.

The next tip concerns a way of verbally working out the doomsday, without the audience being the wiser. Begin by making sure they have a perpetual calendar in front of them. This tip works well with the book Gregorian Calendar Sheets of the Years 1582 - 2399, which allows you to state in advance the page on which a given year's calendar is located.

When you're given a date in the 1900s, work it out as in the Day One instructions, as if it were in the 2000s. When you get that day of the week, immediately state that is the day on which Christmas falls in the given year, then move one day forward and state that this new day is when Halloween falls in that year. The day of the week you give for Halloween is also the day of the week you need to remember.

All at once, then, you've worked out the year information, created the first amazing moment in the routine, adjusted for the 1900s, and even stated the doomsday out loud (making it easier to remember)!

The previous tips all work for any version of Day One, whether you're in a close-up, parlor, or stage venue. The final tip is for stage and parlor, as it involves the use of a large calendar with pockets for holding the month and dates.

The dates 1 through 31 are set up in the calendar as if the 1st of the month fell on a Sunday and the 31st were on a Tuesday. You're holding the cards with the days on them in your hands face-up in Sunday through Saturday order, with Sunday on top facing you, and the bottom-most card being Saturday. The cards with the month names are displayed on a nearby table.

After the audience member gives you the year, you spread the day cards out in your left hand as you work out the doomsday you need. When you get ready to ask them for the month, pick up all the cards above the card showing the doomsday with your right hand, and use those to gesture towards the month cards as you ask them to choose a month card and place it in the topmost pocket of the calendar.

For example, if someone asks for the year 1973, you work out that the doomsday is Wednesday. With the cards already fanned in your left hand, you would pick up all the cards above the Wednesday card (Sunday, Monday, and Tuesday), and use them to gesture towards the month cards and ask them to place one on the calendar.

When you're done making your gesture towards the months, you place the left hand's day cards on top of the right hand's cards and close the spread, so that the doomsday is now showing on top. In our 1973 example, the Wednesday card would be on top at this point. As soon as they choose the month and you recall the month's key date, you're ready to place the day of the week cards in the appropriate spots (as in the standard Day One routine).

This simple and un-emphasized cut of the doomsday card to the top means that you have one less thing to remember in your performance. You no longer have to focus on remembering the doomsday once you've got it, because it's in your hand staring you in the face!

If you've come up with your own clever additional touches for Day One, I'd love to hear about them in the comments!

In March, I briefly mentioned that Joshua Foer, author of Moonwalking with Einstein, gave a talk at TED 2012.

Earlier this month, the people at TED posted the video of the talk online, and it was worth the wait!

The talk is called Feats of memory anyone can do, but it's not a simple lecture on memory technique.

Instead, it's an insight into the world of competitive memorizers. This might sound a little boring, and Joshua Foer points out that watching a memory competition is a little like watching people take their SATs. However, when Joshua got into the mind of memorizers by becoming one himself, it turned out to be anything but dull.

He starts with a demonstration of a basic memory technique, which I highly recommend you try, and takes you on the journey from there. This video is 20 minutes long, but is well worth the time spent. Joshua Foer sums up much of what I've tried to get across in the Grey Matters blog about the fun, power and potential of memory.



Joshua mentions Ed Cooke briefly. If this talk intrigued you, check out Ed Cooke's videos on memory, including his appearance on the How To Do Everything podcast and his TED^x talk.

Wolfram|Alpha's ability to handle numbers is well known, as you may have seen in past posts. But did you know it can also handle English words and letters, too?

In today's post, we'll take a look at the possibilities of solving puzzles with Wolfram|Alpha, by pitting it against some word and number puzzles from our old friend mental_floss.

First up, let's see what Wolfram|Alpha can do against word ladders. Here's one challenging you to change the word CARD to the word FLIP. You can't just ask it to solve the puzzle, but it can help you understand the possibilities.

One of the best strategies is to work inwards from both the top and bottom words, in order to see which words get closer to each other.

Start by entering _ARD into Wolfram|Alpha. You get the words BARD, CARD, DARD, GARD, HARD, LARD, SARD, WARD, and YARD back in response. CARD is the word we're starting with, so that can be eliminated. Dard and Gard are proper nouns, and uncommon, so you can probably eliminate those as possibilities, as well.

Continuing this procedure with C_RD, CA_D, and CAR_, we build up a good list of words to start off with: BARD, HARD, LARD, SARD, WARD, YARD, CORD, CURD, CARE, CARK, CARP, CARS, and CART. Trying the same approach with _LIP, F_IP, FL_P, and FLI_, we build up a list of these words: BLIP, CLIP, SLIP, FLAP, FLOP, and FLIT.

Comparing both lists, CARP and CLIP seem promising candidates, as they begin and end with C and P. Let's ask Wolfram|Alpha about C__P. Eliminating CARP and CLIP themselves, we wind up with the list: CAMP, CHAP, CHIP, CHOP, CLAP, CLOP, COMP, COOP, CORP, COUP, CROP, and CUSP.

The big trick with changing CARP to CLIP seems to be the switching of the vowels and the consonants, so COOP will obviously be a big help here. To get from CARP to COOP, we could use CORP, and to get from COOP to CLIP, we could use CLOP, so that seems to do it! Let's take a look at the word ladder we developed:

CARD
CARP
CORP
COOP
CLOP
CLIP
FLIP

Taking a peek at the answer, we see that we arrived at a different answer, but in the same number of steps!

There are even some word puzzles to which Wolfram|Alpha is extremely well-suited. One such mental_floss quiz involved naming all the non-obscure words of 4 letters or more made from the letters of the word SIXTEEN. Simply give Wolfram|Alpha the command word subsets sixteen, and after it generates the list, sort it by length. After removing any words shorter than 4 letters, proper nouns, and words that could reasonably be considered obscure, you get the words: EXIST, EXITS, INSET, NIXES, STEIN, TEENS, TENSE, TINES, EXIT, NEST, NETS, NEXT, NITS, SEEN, SENT, SINE, SITE, SNIT, TEEN, TEES, TENS, TIES, TINE, and TINS - 24 words in a quiz where 16 is considered a win!

Occasionally, mental_floss offers puzzles with the question “What number comes next in this sequence?”, such as this one. There's a slight problem with these, in that you can set up a formula for any set of numbers.

Let's say I decide that I want 137 to be the next number in the sequence in the puzzle above. I simply set up 9 equations so that each number in the sequence will create a 0 at some point, as follows: (x-1)(x-2)(x-2)(x-4)(x-8)(x-12)(x-96)(x-108)(x-137). When x = 108, you're multiplying by (108 - 108), so you're effectively multiplying everything else by 0.

That equation expanded becomes x⁹ - 370x⁸ + 48509x⁷ - 2636704x⁶ + 53341412x⁵ - 488919184x⁴ + 2206290496x³ - 5008709376x² + 5422344192x - 2181758976. So, you can state that 137 is the next number in that sequence, because it's the next point that, when plotted, crosses the axis at 0 in our formula.

Remember, I just made up the number 137, so it could be any other number just as well. Perhaps you prefer 512? 42? 675? You can find an appropriate formula that will work for any of them. The answers to mental_floss' number sequence puzzles are rarely mathematical in nature. However, our example puzzle happens to be an exception.

Have you solved any mental_floss puzzles by using Wolfram|Alpha to help, or even cheat? I'd love to hear about it in the comments!

One of the oldest versions of Nim is a Chinese game called jiǎn shízǐ, which literally means “picking stones.”

In this particular version, there are two piles of objects of various sizes. On their turn, a player may take either as many objects as they want from just one pile, OR take the same number of objects from both piles. The player who takes the last object wins.

For those familiar with Nim games, this appears to be a minor rule change at first glance. However, a proper analysis of the game yields some surprising principles behind this game.

Completely unfamiliar with the Chinese game, a mathematician named W. A. Wythoff independently reinvented the game, and analyzed the perfect winning strategy back in 1907.

Around 1962, Johns Hopkins University mathematician Rufus P. Isaacs developed a seemingly-unrelated board game using a chess board, often called “Corner the Lady.”

Isaac's game starts with a standard 8 by 8 chessboard or checkerboard, and a single chess queen being placed anywhere in the topmost row, or the rightmost column. The objective is to be the person who moves the queen into the square at the lower right corner. In the image directly below, the black queens represent the possible starting positions for the queen, and the white queen represents the goal square.

I wasn't kidding when I posted that the Knight's Tour has been on my mind recently.

So much so, that I've re-written my Knight's Tour web app from the ground up, and I'm making it available as a free web app as of today!

The new Knight's Tour app is available here. It still features the same 3 challenges as the original version (Landing on all 64 squares, ending a knight's move from your starting point, and ending on a chosen goal square), and now it has even more features!

If you're not already familiar with the Knight's Tour, check out the introduction from my tutorial. This same tutorial is also accessible from the web app's Help menu.

Shortly after the iPhone was released, I developed a version specifically for it, which is still available here. The screen is one size only, and the interface is packed tightly.

That was one of the major reasons for updating my Knight's Tour web app. The new version scales to best fit the available screen space, so the higher the resolution of your computer/mobile device, the bigger the board. If you change your browser size or your device orientation at any time, the board will quickly re-size.

When you first open the app, you'll see the chessboard and you're presented with the Options menu, which can be brought up by either touching/clicking the Options button in the upper left corner (not shown in the picture below), or by touching/clicking the board when no game is being played.



The New Game menu at the top allows you to choose which of the three Knight's Tour variations you wish to play by simply touching/clicking that, and then touching/clicking the appropriate level. The Help button takes you to another menu, where you can learn more about each aspect of the program. The Settings button takes you to another menu which allows you to customize the look and function of the Knight's Tour app.

The Cancel button simply dismisses the menu, which can also be done by touching/clicking anywhere outside of the menu.

Along with the scalable board, the settings are probably the biggest new feature of the Knight's Tour app. Here's an End on Goal Square game being played with the app's default settings: The background is a grey linen-style pattern, and the visited squares are highlighted simply by squares in two different shades of red:



For comparison, below is the same level, but with several settings changed. The background has been changed to a wood pattern, the visited squares are now green, and the path of the knight is now numbered! (Can you see how to finish the game on the target square?)



The other settings include the speed at which the knight moves (From .2 second up to .7 seconds to move to the next square), the ability to turn the algebraic notation (the a8-h1 coordinates) on or off, whether the undo features are available, and even whether you or the app sets up the starting position on the board!

While my original version had Undo features, the new version improves the operation. If the Undo features are on, an undo button will appear in the upper right corner after you move to your second square. Clicking this button will take you back 1 move. You can also undo a move by clicking on the previous square.

You can also have the app ask you to OK each undo, which highlights any backtracking of multiple squares.

The Knight's Tour app will let you know when you're trapped when you land on a square from which you have no possible moves. If the Undo feature is off, this also ends the game immediately.

If the total of each row and column of the numbers formed by your path are all the same number (260), then your Knight's Tour path can be said to form a semi-magic square. If this does happen, the app will automatically notify you of this fact at the end of a complete game. I added this as a sort of bonus feature, so you can grab a screenshot if you ever achieve this.

This is a very rare occurrence, as out of the 10s of trillions of possible knight's tours, only 140 are semi-magic squares. In other words, you're millions of times more likely to get hit by lightning than to accidentally form a semi-magic knight's square by luck. Obviously, this feature will be used more by those who are intentionally trying to create such a square.

Play around with this, and let me know of any comments or criticisms in the comments. I hope you enjoy my Knight's Tour app!

For much of the world, today is Mother's Day!

Is it really possible to mix something as geeky, like memory and math, with the beauty of Mother's Day? You'll find out in today's snippets.

• If you have a geeky heart, you're mother is at least partially responsible. Since she helped give you a geeky heart, why not return the favor? Over at Math Jokes 4 Mathy Folks, one mom shows you how to make a magic square heart. Long time Grey Matters readers and Scam School fans may recognize the magic square principle used to create the heart.

• Maybe your mother likes music? In the video below, Vi Hart plays with mathematical symmetry groups, and gives them a surprising musical twist:



• Perhaps you're giving your mom flowers or plants for Mother's Day? Vi Hart has you covered there, as well. She posted a video series she dubbed Doodling in Math: Spirals, Fibonacci, and Being a Plant. Part 1 is here, followed by Part 2 and Part 3.

• Speaking of music, many people take their mothers out to see musicals for Mother's Day. One classic musical is The Pirates of Penzance, whose best known (and most parodied) song is the Modern Major-General's Song. Even if you're not familiar with the original, you've probably heard it as Tom Lehrer's The Elements, or in some other form. Recently, XKCD took its turn at parodying the song, calling their version Every Major's Terrible. It didn't take long before homemade music video versions of this song flooded YouTube.

• Once again, treat your mother right for Mother's Day. Think of all the times she's taken care of you, even when you were sick:



Happy Mother's Day!

I've been practicing and re-examining the Knight's Tour lately, mostly due to my recent work on Notakto.

In the process, I've run across a few new and fun Knight's Tour videos I thought you might enjoy.

The first clip is from a late '90s British game show called The Moment of Truth. Contestants are given one week to practice some impressive feat, and then perform it before a live audience, often under time pressure, in order to win exotic and expensive prizes.

One of the best things about the video below is that it's a wonderful example of how to create suspense. Between the time clock, the live audience, the player's immediately family, and the possibility of winning prizes, this Knight's Tour has plenty of tension. The anticipation created can be felt strongly.



The next Knight's Tour video is more informational. The basics of the Knight's Tour are explained, and then a example solution is shown. This Knight's Tour video has the rather unusual feature of being shot in 3D! Instead of embedding it, I'll link to the video, so you can use the 3D menu to choose your preferred method of viewing the effect. If you prefer, it can also be viewed as a standard 2D video instead.

The final video in the set is a school lecture about the approaches and history of the Knight's Tour. Just listening to the terminology they use, I can't help but wonder whether these two ran across my Knight's Tour lessons in their research.



While there's not as much tension as the first video, there is plenty to learn from it. As a bonus, you have to love how they chose to end the lecture.

Last month, I posted about a tic-tac-toe-like version of Nim known as Notakto.

That post only discussed how to win the game on a single board. What about winning on more than one board?

Whether or not you've practiced the technique from the previous Notakto post, try the game for yourself. You can play it either online here or download the iPad app here. If you're not familiar with the game, here are the rules, excerpted from the iPad app homepage:

Notakto is a two-player game that is similar to Tic-Tac-Toe, except that both players make X's, and whoever completes three-in-a-row LOSES the game.

For a challenge, play a multiboard game of Notakto. On your move, make an X on just ONE of the boards. The computer may respond on the board you played on, or on some other board. A board that already has a three-in-a-row configuration is considered out of play. To win, force the computer to complete the last three-in-a-row configuration on the last available board still in play.

This is the final post in the age guessing series.

As with the previous post, this will mix the approximate judging of someone's age with math, but this version hides the math better. That's because it focuses on calendar dates!

In this approach, you have a spectator give you their birthday, without the year. You then have the spectator look up the day of the week on which they were born in a perpetual calendar, and tell you that day of the week (again, without telling you the year). You then look them over, and announce their exact age!

For example, let's say your spectator tells you they were born on June 16th. After looking up the day of the week they were born, they tell you it was a Friday. After looking them over briefly, you announce (correctly) that the person was born in 1978!

Basic concepts