# 2021 JMPSC Accuracy Problems/Problem 7

## Problem

If , , and each represent a single digit and they satisfy the equation find .

## Solution

Notice that can only be , , and . However, and are not divisible by , so Thus,

~Bradygho

## Solution 2

Clearly we see does not work, but works with simple guess-and-check. We have , so and . The answer is

~Geometry285

## Solution 3

Easily, we can see that . Therefore,We can see that must be or . If , thenThis doesn't work because isn't divisible by . If , thenTherefore, . So, we have .

- kante314 -

## Solution 4

Notice that the only values of that have for some are and . If , then we have , and so . Notice that is not divisible by , so is not a valid solution. Next, when , we have that . Solving for and tells us that and , so the answer is .

~Mathdreams

## See also

The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.