We solve problems

Problem #PRU-109476

Problems Algebra and arithmetic Word problems Solving problems by inequalities. Going through the cases. Set theory and logic Mathematical logic Mathematical logic (other)

11–14 2.0

Sarah believes that two watermelons are heavier than three melons, Anna believes that three watermelons are heavier than four melons. It is known that one of the girls is right, and the other is mistaken. Is it true that 12 watermelons are heavier than 18 melons? (It is believed that all watermelons weigh the same and all melons weigh the same.)

Problem #PRU-116661

Problems Algebra and arithmetic Word problems Solving problems by inequalities. Going through the cases. Sequences Progressions Arithmetic progression Methods Pigeonhole principle Pigeonhole principle (other) Proof by contradiction

10–12 3.0

Can 100 weights of masses 1, 2, 3, ..., 99, 100 be arranged into 10 piles of different masses so that the following condition is fulfilled: the heavier the pile, the fewer weights in it?

Problem #PRU-30911

Problems Algebra and arithmetic Word problems Solving problems by inequalities. Going through the cases. Geometry Solid geometry Volume Volume of a parallelepiped

11–12 2.0

Will the entire population of the Earth, all buildings and structures on it, fit into a cube with a side length of 3 kilometres?

Problem #PRU-34904

Problems Algebra and arithmetic Word problems Solving problems by inequalities. Going through the cases. Methods Pigeonhole principle Pigeonhole principle (other)

11–14 3.0

Is it possible to transport 50 stone blocks, whose masses are equal to \(370, 372,\dots, 468\) kg, from a quarry on seven 3-tonne trucks?

Problem #PRU-35791

Problems Algebra and arithmetic Word problems Solving problems by inequalities. Going through the cases. Methods Extremal principle Algebraic methods Processes and operations

13–14 3.0

Sam and Lena have several chocolates, each weighing not more than 100 grams. No matter how they share these chocolates, one of them will have a total weight of chocolate that does not exceed 100 grams. What is the maximum total weight of all of the chocolates?