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Counting wins from rock paper scissors tallies

Question

Two players play ten rounds of rock-paper-scissors, and no round is a draw. Over the ten rounds the first player threw rock 33 times, paper once and scissors 66 times; the second threw rock twice, paper 44 times and scissors 44 times. How many rounds did the first player win? Answer −1-1 if this cannot be determined.

Short answer

77. With no draws, the first player's six scissors must meet non-scissors, i.e. all 22 rocks and 44 papers of the opponent, giving 44 wins and 22 losses. The opponent's four scissors then face the first player's 33 rocks (wins) and 11 paper (loss), for 4+3=74+3=7 wins.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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