Show, by giving a proof by contradiction, that if 100 balls are placed in nine boxes, some box contains 12 or more balls.

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Let each box contain less than 12 balls (maximum 11).

Then the maximum number of balls is $11 \cdot 9 = 99$ , which contradicts the condition of the question.

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Question ID: mtid-5-stid-8-sqid-1251-qpid-989