What is the maximum number of enclosed regions that you can create by drawing two circles and two triangles on a flat surface? Try answering with mathematical arguments.


2 Answers 2


I don't have any mathematical arguments, but the best I have managed is 33 regions.

enter image description here

  • $\begingroup$ Congratulations Daniel Mathias! You got it right! $\endgroup$ Commented May 28, 2020 at 23:06

Thanks for the great puzzle!!

The highest I've gotten so far is:

33 regions. Below is a visual representation:


I've also gotten:

32 regions:

Visual representation for 32 regions

30 regions:

30 regions representation

29 Regions:

29 regions

  • $\begingroup$ Ankit, you are very close to the answer. $\endgroup$ Commented May 28, 2020 at 22:46
  • $\begingroup$ I count only 33 regions where you claim 40... $\endgroup$ Commented May 28, 2020 at 23:21
  • $\begingroup$ Ok I'll add something to count it @DanielMathias $\endgroup$
    – Ankit
    Commented May 28, 2020 at 23:25
  • $\begingroup$ Apparently I did miscount... it is 39. The counting is now included in the picture @DanielMathias $\endgroup$
    – Ankit
    Commented May 28, 2020 at 23:33
  • $\begingroup$ Your groups of 10 contain only 8 regions each. $\endgroup$ Commented May 28, 2020 at 23:40

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