1987 AIME Problems/Problem 1

Problem

An ordered pair $\displaystyle (m,n)$ of non-negative integers is called "simple" if the addition $\displaystyle m+n$ in base $\displaystyle 10$ requires no carrying. Find the number of simple ordered pairs of non-negative integers that sum to $\displaystyle 1492$ .

Since no carrying over is allowed, the range of possible values of any digit of $m$ is from $0$ to the respective digit in $1492$ (the values of $n$ are then fixed). Thus, the number of ordered pairs will be $(1 + 1)(4 + 1)(9 + 1)(2 + 1) = 2\cdot 5\cdot 10\cdot 3 = 300$ .