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On Target

Problem

Two players take it in turns to fire at a target. They get six shots each.


Both players scored exactly the same total. If the second player scored 26 points with her first two shots, which player hit the centre?


Solution

The total points on the board for the twelve shots is 152, so each player must have scored 152 ÷ 2 = 76 points with their six shots. If the second player scored 26 points with her first two shots, she must have scored 76 minus 26 = 50 points with her remaining four shots. As both players scored at least one point with each of their shots, it must be player one that hit the centre.

Can you work out precisely how each player scored their 76 points?

Problem ID: 78 (May 2002)     Difficulty: 1 Star

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