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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?

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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.

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  • $\begingroup$ Welcome to Puzzling.SE! Next time please add "spoilers" to significant parts of your answer (I've already added them), so the other users could try to solve the puzzle themselves without accidentally seeing your answer. $\endgroup$
    – trolley813
    Mar 19, 2021 at 19:25

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