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

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 $$7\times7=49$$

• – Git Gud Mar 4 '15 at 15:45
• Consider that 41 in base 12 is 49 in base 10. – Sloan Mar 4 '15 at 15:48
• Hint: Start by cutting off the extra finger. – hardmath Mar 4 '15 at 15:48
• I didn't know the Babylonians had 60 fingers – Rahul Mar 4 '15 at 16:07

## 2 Answers

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

• why do we have $4 \times n + 1$? – Nighty Mar 4 '15 at 16:10
• @LeeKM: because that's how place value works in base $n$. – symplectomorphic Mar 4 '15 at 16:12

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?