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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


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    $\begingroup$ @WeatherVane The four pieces are not necessarily identical. But if they were, that would be nicer. $\endgroup$ Nov 27, 2023 at 19:50
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    $\begingroup$ 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... $\endgroup$
    – Florian F
    Nov 28, 2023 at 20:31
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    $\begingroup$ 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? $\endgroup$ Nov 28, 2023 at 20:39
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    $\begingroup$ 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. $\endgroup$ Nov 29, 2023 at 1:41
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    $\begingroup$ 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. $\endgroup$ Nov 30, 2023 at 5:17

7 Answers 7

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+100
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A very ugly and unorthodox solution

solution

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  • $\begingroup$ This one gets my vote for "most original answer" $\endgroup$ Nov 30, 2023 at 4:06
  • $\begingroup$ 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. $\endgroup$ Nov 30, 2023 at 4:21
  • $\begingroup$ 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. :-) ) $\endgroup$
    – Retudin
    Nov 30, 2023 at 8:22
  • $\begingroup$ @Retudin If you look closely, you may notice that the yellow piece has been flipped. $\endgroup$ Nov 30, 2023 at 12:06
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A solution to the original question, without holes.

enter image description here

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    $\begingroup$ 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. $\endgroup$
    – quarague
    Nov 28, 2023 at 13:02
  • $\begingroup$ @quarague $2^2+4^2=20$ Trial and error not required. $\endgroup$ Nov 28, 2023 at 13:47
  • $\begingroup$ 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!”. $\endgroup$ Nov 28, 2023 at 19:00
  • $\begingroup$ 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. $\endgroup$ Nov 28, 2023 at 20:27
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    $\begingroup$ @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. $\endgroup$ Nov 29, 2023 at 1:47
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Bad drawn simple solution with holes:

enter image description here

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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

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  • $\begingroup$ 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!”. $\endgroup$ Nov 28, 2023 at 19:00
  • $\begingroup$ @WillOctagonGibson apologies $\endgroup$
    – Retudin
    Nov 28, 2023 at 22:44
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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
 

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  • $\begingroup$ 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!”. $\endgroup$ Nov 28, 2023 at 19:03
1
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Quite simple solutions (with holes):

image

image

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  • $\begingroup$ 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!”. $\endgroup$ Nov 28, 2023 at 19:03
1
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Here's an obvious way... but you will probably prefer something without holes.

image

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  • $\begingroup$ Just remove the [1]: part if you want to leave the URL only, or else do something like ![caption](URL). $\endgroup$
    – CiaPan
    Nov 28, 2023 at 10:54
  • $\begingroup$ @CiaPan You definitely do not want URL only. $\endgroup$ Nov 28, 2023 at 12:01
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    $\begingroup$ @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. $\endgroup$
    – CiaPan
    Nov 28, 2023 at 12:22
  • $\begingroup$ 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!”. $\endgroup$ Nov 28, 2023 at 19:01

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