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The Lady or the Lions

The King showed the Princess a map of the maze and the Princess was allowed to decide which room she would wait in. She was not allowed to send a copy to her lover who would have to guess which path to follow. Which room should she wait in to give her lover the greatest chance of finding her?

A Dicey Paradox

Four fair dice are marked differently on their six faces. Choose first ANY one of them. I can always choose another that will give me a better chance of winning. Investigate.

Nine or Ten?

Is a score of 9 more likely than a score of 10 when you roll three dice?

Can't Find a Coin?

Age 11 to 14 Challenge Level:
Imagine your teacher has set you the homework task of throwing a coin 100 times and carefully recording your results in the order that they appear. Imagine that you can't be bothered to go and find a coin - the task is just too tedious. So you decide to try to fool your teacher.

How will you go about it?

One of these students made up their homework results, which one is the most suspicious?


Whilst all combinations of Heads and Tails are equally likely, certain sets of results (such as all heads or alternating Heads and Tails all the way) would look rather suspicious. Why is this?
The computer here is programmed to determine whether the set of Heads and Tails falls into a suspicious category or not. Rather interestingly, if you do generate the Heads and Tails truly randomly using a coin then there is a 95% chance the the computer will know that these were generated randomly. Don't believe it? Try it out!