Five fair slices of a square cake, icing included

Question

A square cake, uniform in height, is iced on its top and on all four sides. Five people want pieces that are equal in cake and equal in icing.

Cutting into five equal strips gives equal cake but unequal icing (the end strips have extra iced sides). Cutting into five equal wedges from the centre to the corners is impossible, since a square only has four corners.

How do you cut it? Every cut is a straight vertical cut from the top of the cake to the bottom.

Accepted Answer

Divide the perimeter of the square into five equal lengths, and cut straight from the centre of the cake to the five division points. Why the cake is equal. Consider one piece: it is the region between two cuts from the centre to the edge, covering a stretch of the perimeter of length L. If that stretch lies along a single side, the piece is a triangle with base L and height equal to half the side of the square, so its area is L times the half-side divided by 2. If the stretch turns a corner, the piece is two such triangles, one on each side, with bases adding to L, and the same formula gives…

Five fair slices of a square cake, icing included

Your answer

Discussion

Learn the concepts

Related questions