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Who pinched the dice? (Posted on 2018-10-04) Difficulty: 3 of 5

My friends and I wanted to play Monopoly, but the dice were missing from the game.

Searching our pockets, we had 4 coins between us, all different: 10c, 50c, $1, and $2.

How can we best emulate a pair of dice with these coins, assuming that they are fair?

No Solution Yet Submitted by broll    
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Some Thoughts re: Why this is difficult | Comment 9 of 10 |
(In reply to Why this is difficult by Jer)

The question was actually about 'best' emulations.

There ia an issue about emulating the dice together or separately, and another, as you have rightly noted, about throwing out results. I could have telegraphed these points in the question, but I didn't want to limit possible approaches.

On the face of it, emulating the dice together is preferable, as it wastes less throws. Throwing out as few as possible results also wastes less throws.

The sort of lines I was thinking along were something like this https://www.youtube.com/watch?v=hBBftD7gq7Y (emulating 2 dice with 3 dice) and this https://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1257524303

Stack exchange also discusses various similar problems, usually with identical coins, or coins one of which is biased.


Edited on October 5, 2018, 12:50 am
  Posted by broll on 2018-10-05 00:45:25

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