Rock Paper Scissors Puzzle

A rock paper scissors puzzle:

  • Anya played 10 games of rock paper scissors against Blake
  • Each time there was a winner (no ties)
  • Anya used rock 2 times, paper 2 times, and scissors 6 times, but you don’t know the order
  • Blake used rock 2 times, paper 4 times, and scissors 4 times, but you don’t know the order

How many games did each player win?


Solution

Anya won 6 times and Bill won 4 times.

Since there were no ties, we know that when Anya played scissors, Blake must have played rock or paper. That means out of the 6 games when Anya played scissors, Anya won 4 and Blake won 2.

That leaves only the games when Blake played scissors, in which Anya played rock 2 times and paper 2 times, so Anya won 2 and Blake won 2.

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