# Operator Square

Probability Level 4

Let the operator $\square$ be defined for all positive integers the following way:

• $1 \square 1=1$.
• For all positive integers $n>1$, $n \square 1=(n-1) \square 1+n$.
• For all positive integers $n>1$, $1 \square {n}=1 \square (n-1)+n$.
• For all positive integers $a>1$ and $b>1$, $a\square{b}=a\square(b-1)+(a-1)\square{b}$.

Evaluate $5\square5$.

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