Doughnut
How can you cut a doughnut into 8 equal pieces with only three cuts
of a knife?
Problem
How can you cut a doughnut into eight equal pieces with only three cuts of a knife?
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Student Solutions
Oliver (Christchurch Cathedral School, UK) has shown his solution clearly in a diagram.
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Plan view  Side View 
Josh (Ampthill, UK) has used words to give the same solution:
Cut in quarters vertically at the top at right angles and then cut horizontally.
Sam (Nanyang Primary School, Singapore) came up with a different approach:
I think that the solution is: You cut the doughnut into halves.
 Then you cut it into quarters.
 Put all the 4 pieces into a stack and cut into halves.
 You will get 8 equal pieces using 3 cuts of a knife.
Teachers' Resources
Why do this problem?
This problem requires a good understanding of the concept of fractions and challenges children to visualise 3D shapes.
Possible approach
You might decide to ask this question orally to start with, without giving the group any visual clues at all. Give pupils time to think on their own, then talk to a partner, then share initial ideas altogether.
In order to come to work on a solution, make sure pairs are encouraged to jot down/draw anything that might be useful.
You could test out ideas at the end with a real doughnut or a bagel!
Key questions
How could you make your first two cuts?
How could you turn the doughnut so you can make another cut?
Possible extension
This sheet gives some ideas for extending the challenge, for example by looking at other 3D shapes, or by focusing on an A4 sheet or paper.
Possible support
Using play dough or plasticene to make a doughnutshape and then to try cutting it, will help children who find the visualisation difficult.