I am puzzled by the below exercise:
Step 1: Select any number having 3 digits (all different from one another). Ex. $125$.
Step 2: Now, write all possible combination of two digit number forming from selected digits. Here it is $12$,$21$,$15$,$51$,$25$,$52$. Add all of them.
here, $ 12+21+15+51+25+52=176$
Step 3: Divide the addition, (here $176$) by sum of all 3 digits selected. i.e.
$ \dfrac{176}{1+2+5} = 22$.
Always. Why, so?
I have tried many combination, it works. Can anyone give proof and explain the reason behind this?