AIME

Discussion on Bangladesh National Math Camp
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Swapnil Barua
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Joined:Tue Apr 13, 2021 2:55 pm
AIME

Unread post by Swapnil Barua » Thu Apr 29, 2021 7:35 pm

Peter, Paul, David join a table tennis tournament. On the first day, two of them were
randomly chosen to play a game against each other. On each subsequent day, the loser of the game on
the previous day would be benched and the other two would play a game. After a certain number of
days, it was found that Peter had won 22 games, Paul had won 20 and David had won 32. How many
games had Peter played?

naso12
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Joined:Mon Jan 09, 2023 11:37 am

Re: AIME

Unread post by naso12 » Mon Jan 09, 2023 11:39 am

I also wanted this. Anyone can help?
Thanks in advance, Best Regards

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asif e elahi
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Joined:Mon Aug 05, 2013 12:36 pm
Location:Sylhet,Bangladesh

Re: AIME

Unread post by asif e elahi » Sat Mar 04, 2023 8:58 am

Every time Peter loses, he doesn't get to play in the next game. So we can (almost) make an one-to-one map between Peter's losing and not playing days. i,e if $x=$ number of games Peter lost, then $x = (22 + 20 + 32) - 22 - x \pm 1 \Rightarrow x=26$. So Peter played $26 + 22 = 48$ games.

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