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King's Maths School

Challenge 468: Paper Cuts

How many pieces of paper result from these folds and cuts?

I have a large square piece of paper. I fold it in half horizontally, then in half vertically, so the resulting piece of paper is 1/4 the original size.

I fold it in half horizontally and vertically again.

Then I fold it in half horizontally and vertically for a third time.

Now I cut my paper in half both horizontally and vertically.

How many separate pieces of paper do I have now?

(If the cutting instruction wasn't clear: after I perform three horizontal and vertical folds, label the midpoints of the four sides of the resulting folded piece of paper. Draw lines joining opposite midpoints. Cut along those lines.)

This is the last WMC of this academic year. You are welcome to send in solutions during the summer holidays, and I will try to reply to any solutions submitted before Friday 7th August.

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.