Given a square, remove one quarter of it. Can the resulting L-shaped figure be divided into 5 congruent shapes? If not, how can we prove that fact?

I tried using circles, triangles and smaller squares, but could not find a solution. Is there a known general solution for any number of divisions, not just 5?

  • $\begingroup$ Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you write what your thoughts are on the problem and include your efforts (work in progress) in this and future posts and in what context you have encountered the problem; this will prevent people from telling you things you already know, and help them give their answers at the right level. $\endgroup$
    – JKnecht
    Commented Feb 29, 2016 at 20:53
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    $\begingroup$ Related, but with four congruent pieces math.stackexchange.com/questions/1420433/… $\endgroup$
    – pjs36
    Commented Feb 29, 2016 at 20:55
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    $\begingroup$ Hi. Yesterday I noticed at page’s tab your question on pleasure and satisfaction by doing mathematics. I guess that you can be interested in a point of view of a mathematician, especially taking into account that that thread contains no accepted answers. So I wrote a short note (in Word) for you and put it here. I hope it can help you at your way. $\endgroup$ Commented Aug 9, 2020 at 16:16
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    $\begingroup$ Alex, Many thanks for sharing your thinking and research on this topic. It will certainly help me on my way forward. $\endgroup$
    – ramana_k
    Commented Aug 10, 2020 at 14:56


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