Puzzle: Non-transitive dice


Consider six dice, each with six numbers on them. The numbers 1 to 36 are distributed between the faces of the six dice. The sum of the numbers on each dice is 111. The six dice are labelled a, b, c, d, e, and f. If I throw two of the dice, X and Y say, and X is more likely to have a higher number than Y, then we say X > Y.

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Are professors and football stars just lucky?

bar sign

You probably have a boss. A manager, an executive, the head honcho. How did they get that position? Was it their skills and knowledge? Or were they just lucky? How about you? Are you where you are because of your expertise, or because of luck? I have no doubt that you deserve your role, but luck may have played a greater role than you think. Especially if you work in a competitive environment.

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Puzzle: Oh no! Puncture!

flat tire

Driving in France recently, I got a puncture in my tyre. I was 13 km from my hotel and needed to get back, but for each kilometre I drove my tyre got flatter, so I had to drive more slowly.

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Probability puzzle: How many balls in the bag?

bouncing balls

Last week our village had a fête. One of the competitions on offer was to guess the number of balls in a bag. There were N balls in the bag, and they were numbered 1, 2, 3, …, N. To help competitors make a sensible guess, they were allowed to take out four balls and note the numbers on them.

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Probability puzzle: Classroom bingo


A primary schoolteacher is playing a game with her class. She has two identical dice, with the numbers on the six faces of each die being 1, 2, 2, 3, 3 and 3. The teacher tells the class that she will throw the pair of dice, add up the two numbers showing, and call out that number in a game of bingo. She then asks each member of the class to make their own bingo card consisting of five numbers of their own choosing.

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