A tennis tournament has 342 players. A single match involves 2 players. The winn

Question

A tennis tournament has 342 players. A single match involves 2 players. The winner of a match will play the winner of a match in the next round, whereas losers are eliminated from the tournament. The 2 players who have won all previous rounds play in the final same, and the winner wins the tournament. What is the total number of matches needed to determine the winner? a. Here is one algorithm to answer this question. Compute 342/2 = 171 to set the number of pairs (matches) in the first round, which results in 171 winners to go on to the second round. Compute 171/2 = 85 with 1 left over, which results in 85 matches in the second round and 85 winners, plus the 1 left over, to go on to the third round. For the third round compute 86/2 = 43, so the third round has 43 matches, and so on. The total number of matches is 171 + 85 + 43 + Finish this process to find the total number of matches. b. Here is another algorithm to solve this problem. Each match results in exactly one loser, so there must be the same number of matches as losers in the tournament. Compute the total number of losers in the entire tournament.

Explanation / Answer

Following the first algorithm we have number of matches as follows:

Round1 ----- 171
Round2-------85 (1 left over)
Round3 ------43
Round4 ------21 (1 left over)
Round5 ------11
Round6 ------5 (1 left over)
Round7 ------3
Round8 ------1 (1 left over)
Round9 ------1

So the total matches = 341

Looking at the second algorithm which says that total number of matches is equal to total number of losers. We have 342 players and as one is winner, there will be 341 losers and hence number of matches is 341.

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