### 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

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:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Take, for example, four consecutive negative numbers, say $$-7, -6, -5, -4$$ Now place $+$ and/or $-$ signs between them.

e.g.

There are many more possibilities. Try to list all of them.

Now work out the solutions to the various calculations.

e.g.

Choose a different set of four consecutive negative numbers and repeat the process.

Take a look at both sets of solutions. Notice anything?
Can you explain any similarities?

Can you predict some of the solutions you will get when you start with a different set of four consecutive negative numbers?
Test out any conjectures you may have.

Can you explain and justify your findings?