1955 AHSME Problems/Problem 37
A three-digit number has, from left to right, the digits , and , with . When the number with the digits reversed is subtracted from the original number, the units' digit in the difference is 4. The next two digits, from right to left, are:
We can set up the subtraction like this: Since , we need to borrow the one from the tens column. Since the result of the tens column is 0, the taken 1 would result in the tens digit being 9:
We can assign a value for and , since that doesn't impact the difference, so lets say that and . Since , we can subtract one from the hundred's digit: Out difference is . Therefore, the next two digits, from right to left, are .
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