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## 'Euler's Officers' printed from http://nrich.maths.org/

How many different solutions can you find to this problem?

Arrange 25 officers, each having one of five different ranks
$a$, $b$, $c$, $d$ and $e$, and belonging to one of five different
regiments $p$, $q$, $r$, $s$ and $t$, in a square formation 5 by 5,
so that each row and each file contains just one officer of each
rank and just one from each regiment.