Let denote a binary operator such that for certain single digit positive integers and , the value of is a unique 3-digit positive integer.
We are given that What is the value of ?
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Let □ denote an operation between a and b , which are two integers. Then, by the pattern, we can see: 1 □ 1 1 □ 2 a □ b = 1 2 ( 1 + 1 ) 1 2 = 1 2 ( 1 + 2 ) 2 2 … = a 2 ( a + b ) b 2