luckydog71 said:
177 amateur tennis players enter a single knock out tennis tournament. There are no draws, all matches are played until a winner is decided. You need to schedule enough tennis matches to be able to declare a winner. How many tennis matches do you need to schedule?
It's not really a riddle, but the answer is 176, as follows:
Round 1 - 79 players receive a bye into the second round; the remaining 98 players play 49 matches, leaving a total of 128 players.
Round 2 - 128 players play 64 matches, leaving 64 survivors
Round 3 - 64 players; 32 matches
Round 4 - 32 players; 16 matches
Round 5 - 16 players; 8 matches
Round 6 - 8 players; 4 matches
Round 7 - 4 players; 2 matches
Round 8 - 2 players; one match
There is another solution, involving no more than one bye in any given round, but the number of games required is still 176 (88, 44, 22, 11, 6, 3, 1, 1).