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A counterexample is an example that disproves a mathematical conjecture or a purported theorem. For example, the Peterson graph is a counterexample to many seemingly plausible conjectures in Graph Theory.

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Odd partition with extra properties

Can such a set $A=$ {$a_1,.. a_k$} exist, such that: $\sum_i a_i = 1$ and $a_i $ are rational positive numbers $k$ is and odd number, and is at least $3$. We can partition $A$ in two parts of value …