## My Favorite Math Puzzle from the US Puzzle Championship

I’ve written about the World Puzzle Championship before.

This is from the US Puzzle Championship in 2001. This particular puzzle was written by Harry Nelson.

High Five

You have a set of five numbers. When adding together each of the ten possible pairs, you get the following sums:

0, 6, 11, 12, 17, 20, 23, 26, 32, 37

What are the five original numbers?

### 5 Responses

1. This isn’t too hard… but I wonder, how would one go about solving a more general problem where the first number is not zero?

2. It’s the interesting generalization (and the simplicity of this) that really caught my eye.

If you want a harder math problem, try Bad Math from the same test (linked above on the number “2001”).

3. I started by adding them, then the zero… it really was easier than I anticipated.

Jonathan

4. […] My Favorite Math Puzzle from the US Puzzle Championship « The Number Warrior […]

5. 4a + 4b + 4c = 4d + 4e = 184
4( a + b + c + d + e ) = 46

a, b, c, d, e (largest to smallest number )
a +b = largest sum
a+ c = second largest number

d + e = smallest number
c + e = second smallest number

That’s all you need. Courtesy of one of my Algebra 2 students.