Limitless football management

4294967296 teams are competing in a football tournament. How many knockout matches should be organized among them to select a winner?

Hint: 2^32=4294967296


The answer is 4294967295.

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3 solutions

Vinayak Iyer
Jan 15, 2015

let it be"n" number of matches, it'll always be the matches - 1

Shiv Ram
Jan 12, 2015

Its just the number of teams n-1

Inderjeet Nair
Dec 26, 2014

according to the given hint 2^32 teams are competing in a football match so initially there will be 2^31 matches to select 2^31 teams, after that there will be 2^30 matches and so on. So the total number of matches = 2^31+2^30+2^29+2^28...2^0. So there are 32 terms to be added with first term as 2^31 and the common ratio as 1/2. Applying the formula to find the sum of terms of an G.P. we get the answer as 2^32-1=4294967295.

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