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Question

The three-digit number whose hundred's digit is the cube of its unit's digit and the ten's digit is the sum of unit's and hundred's digit is ___.

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Solution

Any three digit number can not have its hundred's digit more than 9. If the unit's digit is 'x', then the hundred's digit is x3.
x3<9
x=1 or 2
When x=1, the ten's digit is 1+1=2
When x=2, the ten's digit is 8+2=10 which is greater than 9 and hence x2.
Therefore, the number is 121.

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