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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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possible solution | Comment 2 of 10 |
this process simulates a single die roll, by replication you can then get a pair of dice.


Flip all 4 coins and add up the total of those showing heads.  Continue this process until the total is $1.10 or less.  There are 6 possible totals namely $0, $0.1, $0.5, $0.6, $1, $1.10.  Assign each of these values to a value on the die for example $0 is 1, $0.5 is 2, and so on.  So when you eventually arrive at one of these totals then that is the simulated die roll.  Each is equally likely thus each die value simulated is equally likely.


Do this process a second time to get the value of the second die and you have a simulation of rolling a pair of dice.

  Posted by Daniel on 2018-10-04 07:57:42
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