# 2021 JMPSC Sprint Problems/Problem 5

## Contents

## Problem

What two-digit even number has digits that sum to ?

## Solution

There exists a digit even number that has digits that sum to . Pertaining to the assumption that this operation is in base , there exists only digits to be used, specifically only for the first digit. Only and may be used, as there isn't other pair of digits which sum to

The only two numbers in which satisfy the fact that the digits sum to are and . Yet, only works because it is the only one in which satisfies the condition that the number must be even.

Therefore, is the only two-digit even number that has digits that sum to .

-OofPirate

## Solution 2

The number must have digits and . is odd but is even.

## See also

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