Just when I thought I'd seen every mathematical puzzle there was, along come some new ones!

In this post, we'll take a quick look around the web at some astounding new puzzles that will challenge your mathemathics skill.

I'll start off with one I have run across before in Martin Gardner's books. It's from our old friend James Grime, and concerns the best strategy for playing a simple card game:



Try and work out a good strategy for this game by yourself first. When you want to verify your strategy, or just give up and see the answer, you can watch the follow-up video.

Next up, an impressive game of lying and truth-telling from Scam School. Watch it up to the break, and see if you can work out the logic for yourself before it's explained:



Yes, the above puzzles are variations on classics, so let's turn to the more unusual ones.

From Futility Closet, we have a puzzle concerning what happens when a barge crosses a crumbling aqueduct, with some amusing and admittedly bizarre details thrown in for fun.

Also from the same source, imagine you're given a right triangle, and you draw a square on its hypotenuse. Draw a line that bisects the triangle's right angle, and extend the line all the way through the square. Can you prove whether this line will always bisect the square? As soon as most people hear the phrase “square on the hypotenuse”, the natural assumption is that the answer will involve working through the Pythagorean Theorem. There's a much quicker and simpler way, however.

One good source of mathe puzzles, Mind Your Decisions, has been really going like gangbusters in recent weeks, in terms of releasing mathematical puzzles. Here are my favorites:

1) You have a solid gold bar, marked into 7 equal divisions as follows:

| – | – | – | – | – | – | – |

You need to pay an employee each day for one week. He charges exactly 1 piece of the gold bar per day. You are only allowed to make 2 cuts into the bar (and this is gold so don’t even think about “folding” the bar). How can you make the cuts to pay your worker one gold piece every day?

The answer is in Monday puzzle: paying an employee in gold.

2) You are given a container that holds 24 ounces of ball bearings. You have a balance but no weights for the scale. You want to measure exactly 9 ounces. How can you do it?

The answer is in Monday puzzle: measuring ball bearings.

3) The game is played with a deck of cards numbered 1 to 100, and its rules are as follows. First, you and I each draw one card from the deck and show them face up. Then, I then draw another card from the deck. In the end, I have two cards and you have one. I win the game if either of the following happens:

–The first card I drew is higher than your card

–The second card I drew is higher than the first card I drew

Because I have two different ways to win, I agree to payout more money to compensate for the odds. I will pay you $3 when you win, and you only have to pay me $1 if I win. Are you willing to play this game?

The answer is in Probability question: would you play this card game?.

4) (This is my favorite of the recent Mind Your Decisions posts.) Two friends were getting ready to eat some small snack wraps for lunch. One had 3 wraps, and the other had 5 wraps. A hungry man came along, and convinced the two friends to share their wraps. They cut the 8 wraps into 3 equal pieces, so that everybody could have 8 pieces, and nobody felt treated unfairly.

The hungry man thanked them, and gave them 8 gold coins in payment. The friend with 3 wraps thought the fairest split would be 4 gold coins to both, since the wraps were shared equally. The other friend thought it should be split as 5 and 3, since he had 5 wraps to start, and the other friend only had 3. What is the most fair division of the 8 coins?

The answer is in A fair division storytale.

5) The final puzzle concerns the fair division of land among 4 people, but the problem comes in the fact that the land is a rather unusual shape. You can see both the problem and the answer in Puzzle: how would you divide the land equally?.

If you like this last land-splitting problem, the same blog has another challenging land-splitting puzzle back in a November 2009 column.

How did you do? Were you able to get any of the answers to these on your own?