### Brain Teasers

# Original Number

Take a five-digit number and reverse it. Subtract the original number from the reversed number and you are left with 33957.

How many different possibilities does the original number have?

How many different possibilities does the original number have?

### Hint

Work from the first and last digits.### Answer

Suppose that the original number is abcde. Then edcba-abcde=33957.Since e>a, we must have e=a+3 and therefore d=b+4, and c can be any digit.

a can be 1 to 6 and e 4 to 9, b can be 0 to 5 and d 4 to 9, each pair has 6 possibilities, and c has 10 possibilities.

Therefore, the original number has 6*6*10=360 different possibilities.

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