Skip over navigation
Consecutive Negative Numbers
Age 11 to 14
Challenge Level 
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 |
Related Collections
You may also like
Consecutive Numbers
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Pair Sums
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Negative Dice
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?