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?
Filed under: Mathematics, Puzzles |
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?
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”).
I started by adding them, then the zero… it really was easier than I anticipated.
Jonathan
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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.