## November 2014 riddle

UPDATE (1 December): I thank Amir Sarid for sending me a pointer to the origin of the October 2014 riddle, where follow-ups are also discussed. The details will be given on this month's solution page.

This month's riddle is a follow-up from last month.

Whereas last month the question asked was about the use of two coins, this month we ask the natural follow-up of using only a single coin: which n-sided dice can be simulated using just one coin? (And whereas last month's riddle was a classic, this one is my own invention. It was also brought up as a possibility by several solvers.)

To make the question more interesting, we divide it into two parts. Answer either or both parts. Separate solver lists will be kept for each part.

#### Part 1:

Which n-sided dice can be simulated using just one coin, given that the coin's probability of falling on 'heads' is constrained to be a rational number?

#### Part 2:

Which n-sided dice can be simulated using just one coin, given that the coin's probability of falling on 'heads' is constrained to be an irrational number?

As always, all answers should be accompanied by proofs.

Solvers of Part 2 can get an asterisk next to their names if they can prove that their simulation method requires a number of coin tosses that is within a constant multiplicative factor of the minimal number needed in any simulation strategy that uses only a single, irrational coin.

### List of solvers:

#### Both parts:

Radu-Alexandru Todor (*) (1 November 22:05)
Dan Dima (*) (3 November 22:25)
Li Li (*) (4 November 03:59)
Jan Fricke (*) (10 November 04:17)
Andreas Stiller (14 November 07:37)
Jens Voss (*) (16 November 20:32)
Deron Stewart (19 November 08:45)
Harald Bögeholz (20 November 01:54)
Lorenzo Gianferrari Pini (*) (25 November 00:29)

#### Part 1 only:

Joseph DeVincentis (2 November 08:53)
Ziqi Zhu (4 November 21:23)
Daniel Bitin (5 November 23:09)
Xu Renzhe (8 November 22:07)
Tianxiao Shui (9 November 00:40)
Yuping Luo (24 November 04:51)

#### Part 2 only:

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!