Simple Concept Tough Problem - 3

“If Mathematics is a mile, what you have learnt in a high school is just the first inch ! “

I often utter the above well-known quote in my classes. Pardon me, as I don’t remember whom is this attributed to. Mathematics has no dearth of problems and challenging problems can be posed even with those “inch of mathematics” learnt in a high school. In today’s edition of SCTP, we will see a problem that was asked in the International Mathematical Olympiad 1960 (long time back !). We will see that the solution of this problem requires very basic idea of quadratic equations. So, here goes the problem :

Determine all three digit numbers whci are equal to 11 times the sum of the squares of their digits.

The solution is discussed in the following video :