Wimbledon trivia – but elegant

Mathematics trivia – but I do like the elegant solution.

At Wimbledon the men’s and women’s tournaments each start with 128 players. The question somebody asked yesterday was how many matches would be played in each tournament. Of course the winner would play 7 matches in 7 rounds (2= 128).

The long-winded solution to the total number of matches = 64+32+16+8+4+2+1 = 127

But the elegant solution is, of course, that with 128 players and one winner there are only 127 losers and therefore 127 matches are necessary and sufficient for them to lose.

Clearly with 2participants there must be  2n-1 matches.

And more generally, formulated as a matter of logic,

“In any knockout tournament, the number of matches is one per loser and therefore one less than the number of contestants”


 

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