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TOT 424 1994 Autumn A J1 nuts are placed in boxes

Source:

June 12, 2024
algebracombinatorics

Problem Statement

Nuts are placed in boxes. The mean value of the number of nuts in a box is 1010, and the mean value of the squares of the numbers of nuts in the boxes is less than 10001000. Prove that at least 10%10\% of the boxes are not empty.
(AY Belov)
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