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TOT 310 1991 Autumn A J7 n children divide m identical pieces

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June 9, 2024
combinatorics

Problem Statement

nn children want to divide mm identical pieces of chocolate into equal amounts, each piece being broken not more than once. (a) For what nn is it possible, if m=9m = 9? (b) For what nn and mm is it possible?
(Y. Tschekanov, Moscow)