Here’s
a brain teaser that can be solved with simple math. (As is the case with many math puzzles, there
is more than one way to solve the problem.)
If you think you’re up to it, try to answer the question before reading
the solutions and explanations at the bottom of this page.

__There are 340 players in a__

**tournament. Each game in the tournament is played with 4 people. For each game, there is one winner who moves on to the next round. Rounds will continue until there is just one winner left – the champion. In any round, if the number of players is not a multiple of 4, then some players will be chosen randomly to advance automatically so that the number of people playing in that round is divisible by 4. (This will ensure that each game that is played will have 4 players.) How many total games will be played in the tournament?***SET**
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__Solutions/Explanations____Method 1 (slow)__

To
solve the problem, many people get out pencil and paper and begin calculating
the results, round by round. For each
round, they keep track of the number of games, and then add these up at the end
to find the answer to the question. This
method can be quite time consuming. One
such solution is shown:

__Method 2 (fast)__

Of
course, there is another way to solve this problem – a way that takes much less
time. In the previous solution, the
focus was on the WINNERS from each round.
(The number of players in rounds 2 – 5 was determined by figuring out
how many winners there were in the previous round and adding this amount to the
number of people who were lucky enough to advance automatically.) A much quicker solution involves focusing on
LOSERS:

We
know

**. This means that each game is guaranteed to have 3 losers. The tournament begins with 340 players, and 339 of those players will be a loser at some point. All we need to do is divide 339 by 3 to find our answer: There will be 113 games.***each game that is played will have 4 players*
When
looking at a tough problem, we often hurt ourselves by focusing on the wrong
part of the problem. Sometimes it is
helpful to take a step back, reexamine the problem, and figure out if our focus
is in the right place.

For math tutorials and silly math songs, visit www.onlinemathpro.com

Affiliate Disclosure

For math tutorials and silly math songs, visit www.onlinemathpro.com

Affiliate Disclosure

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