Challenge Level

Take a look at the pattern below:

Can you describe the next few patterns in the sequence?

Can you work out how many squares there are in each pattern?

Is there a quick way to work out the number of squares in the 20th pattern? Or the 50th pattern? Or...

Here's another pattern made from squares:

Can you describe the next few patterns in the sequence?

Can you work out how many squares there are in each pattern?

Is there a quick way to work out the number of squares in the 20th pattern? Or the 50th pattern? Or...

**Can you describe any relationships between the two patterns?**

Here are two similar linked patterns:

Can you find a quick way to work out how many squares there are in these patterns?

**Can you describe any relationships between these two patterns?**

You may wish to look at some similar problems, Seven Squares, Attractive Tablecloths and Steel Cables.

*With thanks to Don Steward, whose ideas formed the basis of this problem.*

Can you describe the next few patterns in the sequence?

Can you work out how many squares there are in each pattern?

Is there a quick way to work out the number of squares in the 20th pattern? Or the 50th pattern? Or...

Here's another pattern made from squares:

Can you describe the next few patterns in the sequence?

Can you work out how many squares there are in each pattern?

Is there a quick way to work out the number of squares in the 20th pattern? Or the 50th pattern? Or...

Here are two similar linked patterns:

Can you find a quick way to work out how many squares there are in these patterns?

You may wish to look at some similar problems, Seven Squares, Attractive Tablecloths and Steel Cables.