You may also like

problem icon

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?

problem icon

Nines and Tens

Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?

problem icon

Racing Odds

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

A Dicey Paradox

Age 11 to 14 Challenge Level:


Four fair dice are marked on their six faces, using the mathematical constants $e$, $\pi$ and $\phi$ as follows:

4 4 4 4 0 0  
B: $\pi \pi \pi \pi \pi \pi$ where $\pi$ is approximately 3.142
C: e e e e 7 7 where e is approximately 2.718
D: 5 5 5 $\phi \phi \phi$ where $\phi $ is approximately 1.618

The game is that we each have one die, we throw the dice once and the highest number wins. I invite you to choose first ANY one of the dice. Then I can always choose another one so that I will have a better chance of winning than you. You may think this is unfair and decide you want to play with the die I chose. In that case I can always chose another one so that I still have a better chance of winning than you. Investigate the probabilities and explain the choices I make in all possible cases.

Does it make any difference if the dice are marked with 3 instead of $\pi$, 2 instead of $e$ and 1 instead of $\phi$?