Three friends, Charles, Hugh, and Freddy, played a one-month tennis tournament, just one match between two of them every single day during last December. During the tournament, whoever lost the day's match took the next day off, while the other two friends played against each other. At the end of the month, Freddy had played 17 matches, including those on his birthday (22nd December) and Christmas Day, both of which he won. Hugh, on the other hand, played one fewer game than Freddy, and also won one fewer game than he did.

Who won the match on New Year's Eve, and who lost it?


On New Year's Eve,

Hugh played Charles

and the winner was



There were 31 matches, so in total everybody played 62 times. Freddy played 17 times, and Hugh one less, so 16 matches. That means Charles has to play 29 matches, almost the entire month; he'll miss only two matches. That means he can lose at most three times, including December 31st, and win the rest of the (at least) 28 matches. Freddy wins at least two times, so Hugh at least once. Together (28+1+2), this counts for all of the wins, and as Freddy won on the 22nd and 25th, Hugh must've won on the 31st, defeating Charles on that day.


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