I am having a hard time figuring out how a circle can be divided into 11 equal parts with only 4 cut allowed? My teacher gave this to us and I still can't cut my pie into eleven equal parts with only four cuts.


Hi Ahmeen,

It IS possible to divide the circle into 11 pieces. I don't see how to make them 'equal' (not equal area at least).

They key is to look at smaller cuts: 2 cuts - how many pieces as a maximum? 3 cuts - how many pieces as a maximum (7!).

What causes the number to DROP - if you change the third cut? What will help the number be as big as possible? If you understand these effects for 3 lines, then you are likely to see how get 4 cuts to make 11 pieces. (Hint - do NOT make all the cuts go through the center of the circle.)

I suspect the 'equal' part was a slip on what is, otherwise, an interesting question which is NOT easy. [I know - I was just marking an assignment on this general question - say for 12 cuts what is the maximum and why? - for a University course ; - ) ]

Walter Whiteley
York University

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