We solve problems

Problems Combinatorics Dissections, partitions, covers and tilings Various dissection problems

Fred and George had two square cakes. Each twin made two straight cuts on his cake from edge to edge. However, one ended up with three pieces, and the other with four. How could this be?

Problem #PRU-103778

Problems Combinatorics Dissections, partitions, covers and tilings Various dissection problems

11–11 2.0

Cut a square into three pieces, from which you can construct a triangle with three acute angles and three different sides.

Problem #PRU-104001

Problems Combinatorics Dissections, partitions, covers and tilings Various dissection problems

12–13 2.0

Kai has a piece of ice in the shape of a “corner” (see the figure). The Snow Queen demanded that Kai cut it into four equal parts. How can he do this?

Problem #PRU-32075

Problems Combinatorics Geometry on grid paper Methods Pigeonhole principle Pigeonhole principle (area and volume) Dissections, partitions, covers and tilings Various dissection problems

12–14 4.0

One corner square was cut from a chessboard. What is the smallest number of equal triangles that can be cut into this shape?

Problem #PRU-87953

Problems Combinatorics Dissections, partitions, covers and tilings Various dissection problems

10–12 2.0

Is it possible to bake a cake that can be divided by one straight cut into 4 pieces?

Problem #PRU-88235

Problems Geometry Plane geometry Convex and non-convex figures Convex polygons Combinatorics Dissections, partitions, covers and tilings Various dissection problems

10–13 3.0

A square piece of paper is cut into 6 pieces, each of which is a convex polygon. 5 of the pieces are lost, leaving only one piece in the form of a regular octagon (see the drawing). Is it possible to reconstruct the original square using just this information?