Olympiad Stuff - combinotorics

21

Arnab Kundu ·2012-04-04 00:28:18

What do you mean by Sum?

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aritraa dfdf ·2012-04-04 00:34:08

by sum i mean the total distance already covrered

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Md. Shahbaz Siddiqi ·2012-04-04 03:17:33

is answer n²(n+1)/2

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11

Shaswata Roy ·2012-04-26 07:57:54

Is it (2n)!n!²

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7

Sigma ·2012-04-27 01:33:00

@Shaswata: ur ans wud hav been correct if the q wud hav been: In how many shortest possible ways can 1 reach the diagonal opp sides of the chessboard??

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21

Shubhodip ·2012-05-17 04:17:32

This is Catalan numbers.

The answer is C_{n-1}

Just look at the permutation matrix and you are done. (Basically a bijection)

I don't have time to explain sorry

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11

sougata nag ·2012-06-03 00:59:57

let the no be g.
then 2g=Î£_1â†’n2r_{C_r}+Î£_{1â‰¤i,jâ‰¤n}i+j_{C_i}

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Shubhodip what
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