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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:
|
A:
|
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 $\phi$?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.