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How can you cut this figure into four (not necessarily identical) pieces which can be reassembled to form a square?

Rotating and flipping the pieces is allowed.

Hole(s) in the final square are allowed.

A nearly square 20-omino

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!

Source of puzzle: https://www.theguardian.com/science/2023/nov/13/can-you-solve-it-are-you-a-lateral-thinker

Will Octagon Gibson
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  • Are they four identical pieces? – Weather Vane Nov 27 '23 at 19:47
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    @WeatherVane The four pieces are not necessarily identical. But if they were, that would be nicer. – Will Octagon Gibson Nov 27 '23 at 19:50
  • Are holes allowed in the final square? – 0x5453 Nov 27 '23 at 19:58
  • @0x5453 Hole(s) in the final square are allowed. If there are two solutions, one with hole(s) and a different solution without holes, I will use my discretion as to which one I will accept. – Will Octagon Gibson Nov 27 '23 at 20:06
  • It's funny that your message about 200 rep and up to not post has never been honored so far in all of your puzzles XD – justhalf Nov 28 '23 at 13:03
  • @justhalf I am disappointed and angry with the answers to this puzzle that came too early. I downvoted them all and left them a note about posting before 48 hours. – Will Octagon Gibson Nov 28 '23 at 19:18
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    Technically you did not forbid it, you only encouraged not to answer. But ok, it is still disappointing. This being said, this must be the only SE site where experts are discouraged to answer to favor less expert answers... – Florian F Nov 28 '23 at 20:31
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    It may be the fact that your question is rather open ended that makes people not feel particularly bad about contributing an answer. After all, it's only one of many that are still available to beginners. Perhaps a more tightly designed puzzle would command more respect? – Albert.Lang Nov 28 '23 at 20:39
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    While I generally agree with you on allowing certain others an opportunity to answer first, 48 hours seems a bit much. I would also argue that any new user wanting to answer will not need such a reservation to do so. Let them get in the same way we did. If they are dedicated, they will earn it. At any rate, as a stipulation for answering it is entirely unenforceable. Spitefully downvoting good and acceptable answers just because you are upset is inappropriate, to say the least. – Daniel Mathias Nov 29 '23 at 01:41
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    For the record, I disagree with all the downvotes this question has received. Up and down votes should be based solely on the quality of the question, and not at all on the asker's actions or opinions. – Daniel Mathias Nov 30 '23 at 05:17
  • @DanielMathias bountying new user's answer so that they no longer satisfy the <200 rep for the Will's subsequent questions? =p – justhalf Nov 30 '23 at 07:31
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    @DanielMathias I downvoted answers while angry. I regret that now. I apologize to all. – Will Octagon Gibson Nov 30 '23 at 08:55

7 Answers7

8

A solution to the original question, without holes.

enter image description here

Daniel Mathias
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    Just a comment on how one might arrive at this solution. The original figure has 20 little squares. So the assembled square should have an edge length of $2\sqrt{5}$. Hence cutting along the edges of the little squares doesn't work but cutting across 2 little squares diagonally gives you an edge of length $\sqrt{5}$. Knowing that one can find this slution with some trial and error. – quarague Nov 28 '23 at 13:02
  • @quarague $2^2+4^2=20$ Trial and error not required. – Daniel Mathias Nov 28 '23 at 13:47
  • In my post I said, “To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!”. – Will Octagon Gibson Nov 28 '23 at 19:00
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    Before posting this puzzle, I was aware of only two solutions and your solution was not one of them. Therefore, your solution could not be the INTENDED solution. – Will Octagon Gibson Nov 28 '23 at 20:27
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    @Will I was surprised that the answer provided in the linked source is not precisely what I have shown. It is, however part of the same class of solutions. Considering that you are not the original author, your claim that my answer could not be the intended solution is just as vacuous as my claim that it is. The problem itself appears to be a variation on a very old puzzle involving a Greek cross. – Daniel Mathias Nov 29 '23 at 01:47
  • Indeed. Here is the Greek cross version of the puzzle. – Jaap Scherphuis Nov 30 '23 at 09:49
8

A very ugly and unorthodox solution

solution

Daniel Mathias
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computer_goblin
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  • This one gets my vote for "most original answer" – Daniel Mathias Nov 30 '23 at 04:06
  • Welcome to PSE (Puzzling Stack Exchange)! One thing that is cool about your solution is that all 4 pieces have different shapes and different areas. – Will Octagon Gibson Nov 30 '23 at 04:21
  • It may be ugly, but answers the question as formulated better than my answer. This considering holes and rotations/flips are explicitly allowed and used here. (Well, no flip; if you had flipped the green piece the answer would be better i.m.h.o. :-) ) – Retudin Nov 30 '23 at 08:22
  • @Retudin If you look closely, you may notice that the yellow piece has been flipped. – Daniel Mathias Nov 30 '23 at 12:06
6

Bad drawn simple solution with holes:

enter image description here

ulutku
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5

An infinite number of less symmetric solutions without holes also exist.

The figure is plain filling (with a square grid of centers.)
One can shift an aligned grid as long as the figure ends up with only 4 parts, like e.g. below enter image description here

Retudin
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  • In my post I said, “To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!”. – Will Octagon Gibson Nov 28 '23 at 19:00
  • @WillOctagonGibson apologies – Retudin Nov 28 '23 at 22:44
2

Here's an obvious way... but you will probably prefer something without holes.

image

theonetruepath
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  • Just remove the [1]: part if you want to leave the URL only, or else do something like ![caption](URL). – CiaPan Nov 28 '23 at 10:54
  • @CiaPan You definitely do not want URL only. – Daniel Mathias Nov 28 '23 at 12:01
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    @DanielMathias An URL alone, used instead of an inserted image, may be another level of protection against inadvertent viewing of the image before the period of 48 hours passes. – CiaPan Nov 28 '23 at 12:22
  • In my post I said, “To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!”. – Will Octagon Gibson Nov 28 '23 at 19:01
2

Quite simple solutions (with holes):

image

image

Daniel Mathias
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CiaPan
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  • In my post I said, “To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!”. – Will Octagon Gibson Nov 28 '23 at 19:03
2

A mildly unorthodox way:

     A                        A
     A A A B B              A A A
     C A B B              C A   B B
     C C D B     -->    C C       B B
   C C D D D              C C   D B
           D                D D D
                              D
Albert.Lang
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  • In my post I said, “To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you!”. – Will Octagon Gibson Nov 28 '23 at 19:03