1. Create every possible two-digit combination.
2. Find their sum.
3. Sum the original three digits.
4. Divide your answer from part 2 by your answer to part 3.

What number do you always get, and why?

Take 3 different digits a, b, and c.

Then all combinations are: ab, ac, ba, bc, ca, and cb

Thus the sum is :

10a + b + 10a +c + 10b + a + 10 b + c + 10c + a + 10c + b

or 22a + 22b + 22c

Thus we have 22(a + b + c) / (a + b + c) = 22