# Dissecting a figure into 2, 3, 4, and 5 parts but not 6

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.

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?

• How can it be proven that a shape cannot be divided into some number of parts? Commented Nov 15, 2021 at 1:15
• 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). Commented Nov 15, 2021 at 1:27
• qph.fs.quoracdn.net/main-qimg-a6d27cf641962cd22f60c30c589aa67d Commented Nov 15, 2021 at 1:45
• 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. Commented Nov 15, 2021 at 18:13
• @IvoBeckers: No that doesn't work at all; it can be divided into 6 identical pieces. =) Commented Nov 22, 2021 at 16:08