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There is a number that is 6 times the sum of its digits. What is this number?
The number is 54, simply because
54 = 6 (5 + 4).
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 = 6 t + 6 u or
4 t = 5 u.
Thus, t / u = 5 / 4. Since t and u are digits, t must be 5 and u must be 4.
Food for thought:
Is the assumption of a 2-digit number a valid one?
Try the Quiz : Puzzles & Brain Teasers : Unique Numbers