Math Is Fun Forum

Mathegocart

Member

Registered: 2012-04-29

Posts: 2,226

Conbinatorics Enigma

In a sports league, there are 20 total teams, divided into 4 divisions of 5 teams each. Over the course of a season, each team plays each of the other teams in its own division 3 times, and each of the other teams in the other divisions twice. How many games does the league have in a complete season?

I said 348 games(12*4)+(150+100+50)=348
(the a.p of 150,100, and 50 comes from a team playing the other divisions twice multiplied by 5(there are 5 teams within each division)
The official solution says 420.
Is it possible to derive 420 utilizing a method similar to mine?

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bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Conbinatorics Enigma

Hi;

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.