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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Weekly Problem 16 - 2012

Weekly Problem 16 - 2012

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Weekly Problem 47 - 2013

Weekly Problem 47 - 2013

Consecutive Negative Numbers

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Well done to Edison, from STC School in Hong Kong, and to Esther, who both sent us correct solutions. Here is Esther's solution:

The first thing I did was to list all the combinations of + and - signs that were possible and then I tried them out on two sets of consecutive negative numbers.

I noticed that the answers to some of them were the same so I tried to work out the general formulae using consecutive numbers $n$, $n+1$, $n+2$, $n+3$.

The results I got are in the table below:

Operations -8, -7, -6, -5 -10, -9, -8, -7 Formula
+ + + -26 -34 4n + 6
+ + - -16 -20 2n
+ - + -14 -18 2n + 2
+ - - -4 -4 -4
- + + -12 -16 2n + 4
- + - -2 -2 -2
- - + 0 0 0
- - - 10 14 -2n - 6