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New here so apologies if this is not quite allowed. Yesterday our department had a meeting in one of our conference rooms on campus. When we arrived the room was empty, but there were three puzzles written on three panels of the whiteboard. Two of them were fairly straightforward number sequences, but we were all left stumped on the third.which is pictured here showing triangle = 3, square = 4, hexagon = 5, circle =?

Would love any suggestions as to a solution or why the hexagon is 5. Thanks!

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    $\begingroup$ To clarify, were the lines through the shapes there originally and do you know if they are part of the puzzle? $\endgroup$ – gabbo1092 May 16 at 15:52
  • $\begingroup$ They were there when we came in, we did not alter what was written at all, but we also don't know if someone else interfered with them after they were originally written. $\endgroup$ – JProblems May 16 at 16:24
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    $\begingroup$ To be fair, that looks like a hexagon that they intended to draw as a pentagon but failed... $\endgroup$ – El-Guest May 16 at 17:30
  • $\begingroup$ @El-guest, ha wouldn't that be nice! $\endgroup$ – JProblems May 16 at 20:04
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One possibility:

If we're looking at polygons and taking the sum of the interior angles, you start with the simplest polygon and then double the sum of the interior angles as you go. So 3 would be 180, 4 would be 360, and 5 would be 720 for the triangle, square and hexagon respectively. I think the lines were added to provide a hint to this conclusion.

As an aside...

Perhaps circle would be 0 as it is not a polygon.

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  • $\begingroup$ I considered this, and you might be right that it's the solution, but it doesn't really give a satisfying connection between the doubling and the indexing. Plus, a circle has 360 degrees, same as the square, so it makes it a strange choice for the next sequence. $\endgroup$ – JProblems May 16 at 20:03

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