The pattern red, white, white, blue, red, white, white, blue, …

Step by step

The question

Question: The pattern red, white, white, blue, red, white, white, blue, ...

keeps repeating.

What is the 48th color?

1 Find the block

The list starts again after blue.

So the block that repeats is red, white, white, blue.

The block is 4 long.

2 Divide

The block comes again and again.

So we divide by its length.

What is left over tells us the place in the block.

4 times 12 is 48.

So 12 full blocks take us to the 48th color.

48 minus 48 is 0 more.

3 Count into the block

Nothing is left over.

So the 48th is the end of a block: the last one, blue.

4 Check

Let's check by counting on.

A block ends at the 44th color.

Then we count on: red, white, white, blue.

The 48th is blue.

So it is right!

Let's look back.

First: find the block.

Then: divide.

Then: count into the block.

Last: check.