Here is a classic teaser, I just want to know how many different ways we have to solve it:Given a n*n chess board, you are in the square of the lower-left corner. For each step, you can either move to the square above or move to the square in the right. Question: how many different routes will lead to the square of the upper-right corner.Any solution is appreciated, however the answer should be explicit.

Am I missing something because it sounds too easy? You have to find the number of sequences consisting of n-1 zeroes and n-1 ones. The answer is obviously

QuoteOriginally posted by: EBalAm I missing something because it sounds too easy? You have to find the number of sequences consisting of n-1 zeroes and n-1 ones. The answer is obviouslyI never said it's difficult. Yesterday someone asked me and I came up with outrun's first method, then he asked me is there any other methods so...

QuoteOriginally posted by: foxkingdomQuoteOriginally posted by: EBalAm I missing something because it sounds too easy? You have to find the number of sequences consisting of n-1 zeroes and n-1 ones. The answer is obviouslyI never said it's difficult. Yesterday someone asked me and I came up with outrun's first method, then he asked me is there any other methods so...Ok. I guess there are many ways to come up with binomial coefficients

QuoteOriginally posted by: EBalQuoteOriginally posted by: foxkingdomQuoteOriginally posted by: EBalAm I missing something because it sounds too easy? You have to find the number of sequences consisting of n-1 zeroes and n-1 ones. The answer is obviouslyI never said it's difficult. Yesterday someone asked me and I came up with outrun's first method, then he asked me is there any other methods so...Ok. I guess there are many ways to come up with binomial coefficients essentially (positive integer) binomial coefficents and pascal's triangle are the same thing. I can't think of any other way to do this...