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Unique Numbers

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There is a number that is 3 times the sum of its digits. What is this number?
Answer: 27

Solution:

The number is 27, simply because
27 = 3 (2 + 7).

How does one find this number?

Let t be the digit in the tens place and u be the digit in the units place. Then, the number is 10 t + u, and the sum of its digits is t + u. The following equation can be readily written:

10 t + u = 3 t + 3 u or
7 t = 2 u.

Thus, t / u = 2 / 7. Since t and u are digits, t must be 2 and u must be 7.

Food for thought:

Is the assumption of a 2-digit number a valid one?


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