( X Y + Y X ) (XY+ YX ) % 7?

If the number 16 is added to its reverse, 16 + 61 = 77 16+ 61= 77 .
The sum is 77 which is divisible by 7.
But you will not find many numbers have this property.
For example 15 + 51 = 66 15 + 51 = 66 , which is not divisible by 7.
How many two digit-number has this properties?

Assume that 05 05 is not a two-digit number.


The answer is 11.

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1 solution

Ossama Ismail
Feb 13, 2016

XY + YX = 11 * (X+Y)

solve (X + Y) = 7 or 14

1- 16, 61

2- 25 ,52

3- 34, 43

4-59, 95

5- 68, 86

6- 77

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