### 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?

# Consecutive Negative Numbers

##### Age 11 to 14Challenge 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