After login you will be able to create your own lists of problems.

Problems

Sort

Age

Difficulty

Clear filters

Found: 5

Problem #PRU-103778

Problems Discrete Mathematics 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 Discrete Mathematics 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 Discrete Mathematics 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 Discrete Mathematics 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 Discrete Mathematics 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?