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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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attempt at simplicity | Comment 4 of 10 |
Pick 3 coins, say 50,100,200c. Assign them binary values: 50 is the rightmost bit, 100 the middle bit and 200 the leftmost bit. Heads=1,Tails=0. Flip all three and generate a binary number 0 to 7.
If 0 or 7 come up, ignore this and flip again. Otherwise you have 1 to 6 with uniform probability. That's 1 die. Repeat to get the second die and add.  

If binary is foreign to them, then instead do this after flipping the 3 coins specified: Sum the value of the heads-up coins only. Double the total as expressed in dollars. This also generates 0,1,...7 uniformly. 

Edited on October 4, 2018, 10:31 am
  Posted by Steven Lord on 2018-10-04 08:55:57

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