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More balanced weighings with 100 coins than with 99

Source: Indian RMO, Paper 2, Problem 6

December 11, 2013
functionmodular arithmeticcombinatorics unsolvedcombinatorics

Problem Statement

For a natural number nn, let T(n)T(n) denote the number of ways we can place nn objects of weights 1,2,⋯ ,n1,2,\cdots, n on a balance such that the sum of the weights in each pan is the same. Prove that T(100)>T(99)T(100) > T(99).
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