4
$\begingroup$

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 $7\times7=49$

$\endgroup$
  • $\begingroup$ Puzzling Stack Exchange. $\endgroup$ – Git Gud Mar 4 '15 at 15:45
  • $\begingroup$ Consider that 41 in base 12 is 49 in base 10. $\endgroup$ – Sloan Mar 4 '15 at 15:48
  • 5
    $\begingroup$ Hint: Start by cutting off the extra finger. $\endgroup$ – hardmath Mar 4 '15 at 15:48
  • 5
    $\begingroup$ I didn't know the Babylonians had 60 fingers $\endgroup$ – Rahul Mar 4 '15 at 16:07
9
$\begingroup$

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

$\endgroup$
  • $\begingroup$ why do we have $4 \times n + 1$? $\endgroup$ – Nighty Mar 4 '15 at 16:10
  • 1
    $\begingroup$ @LeeKM: because that's how place value works in base $n$. $\endgroup$ – symplectomorphic Mar 4 '15 at 16:12
7
$\begingroup$

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?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.