A dice that has n sides is, conceptually, a device that allows one to
allot a number between 1 and n, each with probability 1/n. For
example, the cubic dice, the most common dice, does this with n=6.
You don't actually need a dice to attain this effect. For example, a cubic dice can be simulated by two coins: one fair coin, with 1:1 probability of landing on heads vs. tails, and the other a biased coin, with 1:2 probability.
To determine the value of a dice throw, first toss the biased coin. If it
lands on heads (which happens with probability 1/3), set This is, of course, not the only way to simulate a cubic dice, and the algorithm is given here merely as an illustration. The main feature to note about this algorithm is that it terminates in finite, bounded time (i.e., total number of coin tosses), always, regardless of the result of any coin tosses. This is a feature we will require of all simulations.
This month's question: is it always possible to simulate an
If it is not always possible to create such a simulation for every |
## List of solvers:Yuping Luo (2 October 04:33)Radu-Alexandru Todor (2 October 08:08) Oded Margalit (5 October 07:55) Daniel Bitin (6 October 20:36) Jens Voss (10 October 06:02) Deron Stewart (11 October 10:49) Li Li (13 October 03:10) Lorenzo Gianferrari Pini (15 October 03:32) Dan Dima (30 October 02:00) |

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The solution will be published at the end of the month.

Enjoy!