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Suppose the vertices of the pentagon are A, B, C, D and E.

Put the numbers 1 and 10 between (not at) A and B so side AB = 11

Put the numbers 2 and 9 between (not at) B and C so side BC = 11

Put the numbers 3 and 8 between (not at) C and D so side CD = 11

Put the numbers 4 and 7 between (not at) D and E so side DE = 11

Put the numbers 5 and 6 between (not at) E and A so side EA = 11.

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