An alien comes to Earth and says $7\times7=41$. How many fingers does he have?

Question

I understand this sounds ridiculous at first but I got asked this question by a supply teacher $3$ days ago and I haven't been able to answer it so it's driving me insane.

I got given two hints:

It's over $10$ fingers
because we have $10$ fingers we count in base $10$ which is why for us $7\times7=49$

Consider that 41 in base 12 is 49 in base 10. – Sloan Mar 04 '15 at 15:48 — Sloan, Mar 04 '15 at 15:48
Hint: Start by cutting off the extra finger. – hardmath Mar 04 '15 at 15:48 — hardmath, Mar 04 '15 at 15:48
I didn't know the Babylonians had 60 fingers – Mar 04 '15 at 16:07 — , Mar 04 '15 at 16:07
This is not what you should do if an alien comes to Earth. – DanielV Jul 31 '20 at 19:28 — DanielV, Jul 31 '20 at 19:28

score 9 · Answer 1 · answered Mar 04 '15 at 15:48

9

The question is equivalent to $ 7 \times 7 = 4 \times n + 1 $, and solve for $n$ (the number of fingers). Hence $n = 12$.

answered Mar 04 '15 at 15:48

LaBird

1,018

why do we have $4 \times n + 1$? – Nighty Mar 04 '15 at 16:10
1

@LeeKM: because that's how place value works in base $n$. – symplectomorphic Mar 04 '15 at 16:12

3d0 · Answer 2 · 2018-03-23T21:00:59.460

7

7x7 = 49 in base 10. If the alien says it's 41, it's base is higher. If we try with base 12

$$ 49 / 12 = 4 \land 49 \% 12 = 1 \implies 49_{10} = 41_{12} $$

But how many hands does it has? One? two? ten? Are they evenly distributed? Let's just assume they are humanoid, so two hands, therefore six fingers per hand?

edited Mar 23 '18 at 21:00

answered Mar 04 '15 at 15:50

3d0

676

An alien comes to Earth and says $7\times7=41$. How many fingers does he have?

2 Answers2