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There is a number that is 8 times the sum of its digits. What is this number?
Answer: 72
Solution:
The number is 72, simply because
72 = 8 (7 + 2).
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 = 8 t + 8 u or
2 t = 7 u.
Thus, t / u = 7 / 2. Since t and u are digits, t must be 7 and u must be 2.
Food for thought:
Is the assumption of a 2digit number a valid one?
Try the Quiz : Puzzles & Brain Teasers : Unique Numbers
