# Blog

## Brainteaser: Patchwork problem

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Difficulty: Tricky

Jack is making a quilt from only square patches of fabric. For every 4 patches he sews together, 1 patch is blue and 3 patches are red. Once they are added to the quilt, all of the patches are 5 cm in width and length. Jack wants to make a quilt that is 100 cm by 50 cm.

How many blue patches will he need?

## Need a hint?

You can break this question down into two parts – First, working out how many squares there are in the quilt, and then working out how many are red.
This isn’t the only way to solve it though!

## Brainteaser answer

Jack will need 50 blue patches to make his quilt.

There are many ways to solve this puzzle – one way is to start by calculating how many squares run along each side of the quilt.

The longer edge of the quilt is 100 cm. We can divide by the size of one square, 5 cm, to find out how many squares long it is: 100÷5 = 20.

We can follow the same process for the short side: 50 cm divided by 5 equals 10 patches long.

Next, we can multiply the two dimensions in patches to find how many total patches make the area of the quilt: 20 times 10 = 200 total patches in the finished quilt.

Now we use the information that 1 patch in every 4 is blue. In other words, ¼ of the patches are blue. If we multiply 200 by 1/4, we get 50! So, Jack needs 50 blue patches to finish his quilt.

You could also solve it using areas. First find the area of the quilt: 100 cm times 50 cm, which equals 5,000 cm squared.

Next, ask how many patches fit inside that area. Each patch is 5 cm by 5 cm so the area of each patch is 25 cm squared.

Notice that we now have two areas with the same unit: cm squared. This means we can divide the whole quilt area by the patch area to find the number of patches that make up the quilt: 5,000 divided by 25 is 200. So, there are 200 patches in the finished quilt.

Now we use the information that 1 patch in every 4 is blue. In other words, ¼ of the patches are blue. If we multiply 200 by 1/4, we get 50! So, Jack needs 50 blue patches to finish his quilt.

Did you find the answer a different way? Tell us in the comments!

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