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Vandaag is het 1 October 2022

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Risk tournament - math puzzle


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The great Risk tournament is organized again. This year there are 1000 contestants. Each game in the tournament is played with 4 people. After each game, there will be one winner which goes to the next round. In the next round again groups of 4 players are formed. If one does not get an exact multiple of 4 in this way, some of the players in this round are selected randomly. These players can go to the following round automatically. In the end there will be one winner. How many games will be played?


After each game, there are of course 3 losers. In the end there will be 999 losers. The number of played games is hence 999 divided by 3 is 333.
A less elegant way to the solution is to calculated the number of games directly. In the first round there will be played 1000 / 4 = 250 games, in the second 62 (since 62*4 = 248, 2 players are selected at random to pass to the third round), in the third round 64 / 4 = 16, in the fourth round 16 / 4 = 4 and in the fifth round 4 / 4 = 1. In total 250+62+16+4+1=333 games.