This figure is divided in 2, 3 and 4 equal parts of same size and shape, but it is not possible to do it in 5 equal parts of same size and shape.

In 2 In 3 In 4

Is it possible to find a figure that can be divided in 2, 3, 4 and 5 equal parts of same size and shape but not in 6?

  • 4
    $\begingroup$ How can it be proven that a shape cannot be divided into some number of parts? $\endgroup$
    – bobble
    Nov 15, 2021 at 1:15
  • 3
    $\begingroup$ If the shape of the pieces created by slicing something into 3 is symmetrical, you can always have 6 slices (cut each one along that line of symmetry). $\endgroup$ Nov 15, 2021 at 1:27
  • 4
    $\begingroup$ qph.fs.quoracdn.net/main-qimg-a6d27cf641962cd22f60c30c589aa67d $\endgroup$
    – msh210
    Nov 15, 2021 at 1:45
  • 2
    $\begingroup$ You haven't defined what a "part" means. For example, can it be a nonmesurable set? Even if you have a definition of "part", you still need to give a proof that it cannot be divided into five parts. $\endgroup$
    – WhatsUp
    Nov 15, 2021 at 18:13
  • 2
    $\begingroup$ @IvoBeckers: No that doesn't work at all; it can be divided into 6 identical pieces. =) $\endgroup$
    – user21820
    Nov 22, 2021 at 16:08


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