12
$\begingroup$

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?

$\endgroup$
17
  • 4
    $\begingroup$ How can it be proven that a shape cannot be divided into some number of parts? $\endgroup$
    – bobble
    Commented Nov 15, 2021 at 1:15
  • 5
    $\begingroup$ 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). $\endgroup$ Commented Nov 15, 2021 at 1:27
  • 5
    $\begingroup$ qph.fs.quoracdn.net/main-qimg-a6d27cf641962cd22f60c30c589aa67d $\endgroup$
    – msh210
    Commented 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
    Commented 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
    Commented Nov 22, 2021 at 16:08

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.