I'm not quite sure how to even start this problem. I'm really just looking for direction on how to begin.
The $t$ mutually orthogonal Latin squares $A_1, A_2, ... , A_t$ of side $n$ have mutually orthogonal subsquares $ S_1, S_2, ... S_t$ occupying their upper left $s$x$s$ corners. Prove that $n$ is greater than or equal to $(t+1)s$.
I know that $t$ must be less than $n$, but I can't find any other information to help me.