Brain Teaser

Question

What's the minimum number of straight cuts required to cut a circle into 7 regions of equal area?


Answer

There are a number of ways to do this with 4 cuts. Here’s one example:

The first vertical cut cut contains 1/7 of the pizza (to the left), while the other two vertical cuts create 3 regions of 2/7 of the pizza, which are then bisected by the horizontal cut. Can you find other examples with 4 cuts?

On the other hand, this is impossible to do with 3 (or fewer) cuts. as that would require 3 chords each having an area of 3/7 of the whole pizza cutting each other into thirds, or 6 pieces with a crust and 1 in the center. For reasons of symmetry, the chords will have to be at 60 degrees apart, which uniquely determines the unequal areas of the regions, as shown below.

  • Problem by Michael Mendrin
  • Solution by Pietro Toniolo & Michael Mendrin
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