Challenge Level

Choose any three whole numbers, find the differences between them all, and find the product of the differences.

For example, if your three whole numbers are $7$, $4$ and $12$, the differences are:

$12 - 7 = 5$

$12 - 4 = 8$

$7 - 4 = 3$

The product of the differences is

$3\times 5\times 8 = 120$

Try a few examples.

**What do you notice?
Can you explain what you've noticed?**

Now choose any four whole numbers, find the differences between them all, and find the product of the differences.

For example, if your four whole numbers are $7$, $4$, $12$ and $6$, the differences are:

$7-4 = 3$

$12-7 = 5$

$7-6 = 1$

$12-4 = 8$

$6-4 = 2$

$12-6 = 6$

The product of the differences is $3\times 5\times 1\times 8\times 2\times 6 = 1440$

Try a few examples.

**What do you notice?
Can you explain what you've noticed?**