Q: (Jun 30) Math counting problem about tennis matching

Q: A singles tennis tournament (one against one) is organized with 100 participants. It takes place in direct elimination (If the number of players is odd, the last is qualified automatically). How many games will be played to determine the winner?

A:

Say 100 participants got paired off into 100/2 = 50 pairs.

There will be 50 games played in the first round.

There will be 25 pairs matched for round 2 from those 50 winners from the 50 pairs in round 1. There will then be 25 games played in round 2 with 25 winners.

Now there is an odd amount of people, so only 24 people are matched and thus 12 games are played in 3rd round with 12 winners.

Next round (4th) will have 6 games played with 6 winners, then after that the 5th round will have 3 games played and 3 winners. The leftover 25th person from round 3 (who won round 2), will now pair with the 3rd person for round 6, while the other twos match, so there will be 2games played in round 6 with 2 winners.

Round 7 aka the final will have 1 game and 1 absolute winner. There are then: 50+25+12+6+3+2+1 = 99 games