If there is a set of an odd number of integers such that removing any one of them allows the remaining integers to be partitioned into two subsets of equal sum and equal size, are all the original integers necessarily equal?
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Do you mean they have the same sum regardless of which element we remove? Otherwise all three integer sets will have this property. – CyclotomicField May 01 '24 at 03:08
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What have you tried so far? – ultralegend5385 May 01 '24 at 03:11
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The response to the first comment is yes.In the case of an odd number of non-negative integers and non-negative rational numbers, the proof can be established using infinite descent. – Syobon1 May 01 '24 at 03:16
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@CyclotomicField There might be misunderstanding? For example from ${0,1,2}$, removing $2$, and the two singleton partitions of ${0,1}$ have different sums. – peterwhy May 01 '24 at 03:18
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That’s correct.I appreciate！ – Syobon1 May 01 '24 at 03:19