Question

Find a 2-digit number smaller than 50, the sum of whose digits does not change after being multiplied by a number greater than 1

Answer 1

To solve this question, it is needed to know that the sum of the digits of numbers which are multiples of 9 greater than 1, add to 9, that is:

Multiples of 9:

9*1 = 9

9*2 = 18 -> 1 + 8 = 9

9*3 = 27 -> 2 + 7 = 9

9*4 = 36 -> 3 + 6 = 9

9*5 = 45 -> 4 + 5 = 9

Find a number:

Thus, there are 4 possible options for the desired 2-digit number less than 50:

18, 27, 36, 45.

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