# 1987 AJHSME Problems/Problem 8

Revision as of 21:25, 10 March 2009 by 5849206328x (talk | contribs) (New page: ==Problem== If <math>\text{A}</math> and <math>\text{B}</math> are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is <cmath>\...)

## Problem

If and are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is

## Solution

The minimum possible value of this sum is when , which is

The largest possible value of the sum is when , making the sum

Since all the possible sums are between and , they must have digits.