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Found: 55

Problems Algebra and arithmetic Number theory. Divisibility Odd and even numbers Combinatorics Dissections, partitions, covers and tilings Tilings with ordinary and domino tiles

10–12 2.0

Is it possible to fill a \(5 \times 5\) board with \(1 \times 2\) dominoes?

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-34970

Problems Combinatorics Dissections, partitions, covers and tilings Covers Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

13–14 3.0

Some open sectors – that is sectors of circles with infinite radii – completely cover a plane. Prove that the sum of the angles of these sectors is no less than \(360^\circ\).

Problem #PRU-35058

Problems Combinatorics Dissections, partitions, covers and tilings Covers Methods Pigeonhole principle Pigeonhole principle (area and volume)

13–15 3.0

10 magazines lie on a coffee table, completely covering it. Prove that you can remove five of them so that the remaining magazines will cover at least half of the table.

Problem #PRU-35795

Problems Combinatorics Dissections, partitions, covers and tilings Covers Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

12–14 2.0

A straight corridor of length 100 m is covered with 20 rugs that have a total length of 1 km. The width of each rug is equal to the width of the corridor. What is the longest possible total length of corridor that is not covered by a rug?