Latin Squares!

Computer Science Level 5

Given above is a 5 × 5 5 \times 5 grid. In how many ways can you fill the grid with numbers from 1 1 to 5 5 inclusive such that each number appears exactly once in each row and column?

Details and Assumptions

  • Every number from 1 1 to 5 5 inclusive must be used exactly five times in the entire grid.

  • An explicit example of such grid -


The answer is 161280.

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Arulx Z by Arulx Z , 20, India

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1 solution

Peter Macgregor
Jul 27, 2015

I haven't been able to find (much less work out!) a simple formula for the number of Latin squares. However the answer 161280 lies in the OEIS

http://oeis.org/A002860

1 Helpful 0 Interesting 0 Brilliant 0 Confused

According to Wikipedia there actually is no easily computable formula! The only solutions involve literally running through all the possibilities, which becomes increasingly difficult to do for greater grid sizes.

Garrett Clarke - 5 years, 10 months ago

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