Pair Products

Choose four consecutive whole numbers, for example, $4$, $5$, $6$ and $7$.

Multiply the first and last numbers together.

Multiply the middle pair together.

Choose different sets of four consecutive whole numbers and do the same.

What do you notice?

Choose five consecutive whole numbers, for example, $3$, $4$, $5$, $6$ and $7$.

Multiply the first and last numbers together.

Multiply the second and fourth numbers together.

Choose different sets of five consecutive whole numbers and do the same.

What do you notice now?

What happens when you take $6, 7, 8, \ldots n$ consecutive whole numbers and compare the product of the first and last numbers with the product of the second and penultimate numbers?

Explain your findings.

A poster of this problem can be found here.