You may also like

problem icon

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

problem icon

Pair Sums

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

problem icon

Negative Dice

Weekly Problem 16 - 2012
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

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