This month's riddle is a follow-up from last month
and the month before it. It was suggested by
Radu-Alexandru Todor and Lorenzo Gianferrari Pini. (Thanks!)
This month's riddle comes in two parts. Answer either or both parts. Separate solver lists will be kept for each part. ## Part 1:Let a "casino" be a point,p, on the interval [0,1], such that for any
integer n≥2 and for any open neighbourhood N of p
there is a point p in _{n}N such that the
n-sided dice can be simulated by a biased coin with probability
p in a finite number of throws.
_{n}Characterise exactly (with proof) the subset of [0,1] that is the set of casinos. ## Part 2:
Let a "rational casino" be a point (not necessarily rational-valued),
( q) in _{n}N, such that a pair of
biased coins with probabilities p and _{n}q,
respectively, can simulate an _{n}n-sided dice in a finite number of throws.
Find (with proof) one such rational casino.
An asterisk will be given to solvers able to characterise exactly the subset of
[0,1] |
## List of solvers:## Part 1:Li Li (16 December 10:28)## Part 2:Harald Bögeholz (10 December 23:27)Dan Dima (12 December 08:58) Li Li (*) (16 December 10:28) |

Elegant and original solutions can be submitted to the puzzlemaster at __riddlesbrand.scso.com__.
Names of solvers will be posted on this page. Notify if you don't want
your name to be mentioned.

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

Enjoy!