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Today Puzzle #549

Puzzle No. 549– Tuesday 20 August

Ten people meet for a dinner party. All of them have at least one friend at the party. Must there be two people at the party with the same number of friends at the party?

Today’s #PuzzleForToday has been set by the School of Mathematics and Statistics at the University of Sheffield.

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Yes; two people necessarily have the same number of friends at the party. All ten party-goers have between 1 and 9 friends at the party and the ten people can't all hold a different number between 1 and 9.

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