Answer to January 29, 2001 Problem

from The Car Talk Radio Show (1995)

The Alien Math Class Problem

 
Two Winchester astronomers were looking through a telescope and observed an alien mathematics class.
On the blackboard, the following equations were written:

13 + 15 = 31
10 x 10 = 100
6 x 3 = 24

One astronomer said to the other, "How many fingers do they have?"

What is the answer to that question? Explain.

 

Solution to Problem:
The answer is seven.

First, observe that seven numerals are used in the equations:
0, 1, 2, 3, 4, 5, and 6.

So I began with base seven and noticed that all three equations were correct in that number system.
If the three equations had not worked in base 7, I would have tried base 8, then base 9, ... 

  
 In base 7              In base 10  
--------------         --------------
 13 + 15 = 31   ===>    10 + 12 = 22
 10 x 10 = 100  ===>      7 x 7 = 49
   6 x 3 = 24   ===>      6 x 3 = 18


Correctly solved by:

1. Vickie Francis -----
2. Kirstine Wynn Winchester, VA
3. Chip Schweikarth Winchester, VA
4. Chad McDaniel Winchester, VA
5. Matthias Switzerland
6. George Gaither Winchester, VA
7. Tony Alteparmakian Bakersfield, CA
8. David Powell Winchester, VA
9. Tom Kelley Winchester, VA
10. Erin McGinnis Winchester, VA