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.

  • $\begingroup$ Can you please clarify what you mean by "bounded regions" and "to the maximum"? I think you mean the maximum number of completely-enclosed shapes (with sides from the circles+triangles), but it is not completely clear. $\endgroup$ – bobble May 28 '20 at 20:23
  • $\begingroup$ You are right bobble. I’m sorry that I wasn’t clear enough. $\endgroup$ – Display maths May 28 '20 at 20:25

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! $\endgroup$ – Display maths May 28 '20 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. $\endgroup$ – Display maths May 28 '20 at 22:46
  • $\begingroup$ I count only 33 regions where you claim 40... $\endgroup$ – Daniel Mathias May 28 '20 at 23:21
  • $\begingroup$ Ok I'll add something to count it @DanielMathias $\endgroup$ – Ankit May 28 '20 at 23:25
  • $\begingroup$ Apparently I did miscount... it is 39. The counting is now included in the picture @DanielMathias $\endgroup$ – Ankit May 28 '20 at 23:33
  • $\begingroup$ Your groups of 10 contain only 8 regions each. $\endgroup$ – Daniel Mathias May 28 '20 at 23:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.