Question

Think of a 2-digit number, Reverse the digits and add it to your original number that is a multiple of 11, why? (with proof)

Answer 1

You can write original number as :

x = 10 a + b

Reverse number you can write as :

y = 10 b + a


x + y = 10 a + b + 10 b + a = 11 a + 11 b = 11 ( a + b )


Example :

Original number:

x = 23

a = 2 , b = 3

x = 10 a + b = 10 * 2 + 3 = 20 + 3 = 23

Reverse number:

y = 10 b + a = 10 * 3 + 2 = 30 + 2 = 32


x + y = 23 + 32 = 55

Answer 2

55 = 11 * 5