# Find the pattern of the following series: 7 × 3 = 5? [closed]

I recently came across a certain question which I was not able to solve.

It was as follows:

7 × 3 = 5
9 × 5 = 41
15 × 11 = ??

Can you tell me the logic behind this?

The rule is:

Take the "normal" multiplication, and sum the squares of the digits

Explicitly:

$$7 \times 3 = 21; 2^2 + 1^2 = 5,$$

$$9 \times 5 = 45; 4^2 + 5^2 = 41$$

and so

$$15 \times 11 = 165; 1^2 + 6^2 + 5^2 = 62.$$

Of course, with a question like this there's no way to know for sure that this is the definitive 'right' answer, as you could come up with any number of different rules that give $$7 \times 3 = 5$$ and $$9 \times 5 = 41$$. But this "feels'' like it's the intended solution.