Cube + reason - practice problems
Number of problems found: 28
- Variations 3rd class
From how many elements can we create 13,800 variations of the 3rd class without repeating? - Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - Red cubes
There are 15 white and several red cubes in the box. The probability of accidentally pulling out a white cube is 20%. How many red cubes are in the box? - Integer cube
The length of the cube edge is an integer. Its volume is in cm3, a five-digit number divisible by 1331. What is the length of the edge of this cube? - Points 2836
Three dice throw a total of 12. Green has two times more than red. Blue is two times less than green. How many points are on each cube? - Product 3108
The product of 3 numbers is 42. The first is 1.5 times larger than the second number, and the third is 3.5 times larger than the second number. What numbers are these? - Indistinguishable 81481
How many ways can a tower of five yellow and four blue cubes be built so that each yellow cube is adjacent to at least one other yellow cube? Yellow dice are indistinguishable, and so are blue dice. - Lengthwise 2144
The mouse has 27 cubes, which it puts together in a large cube. Then she bit the middle cat on each side and another cat in the middle. The mouse has four children. He then cuts the cube lengthwise. How many cubes and what shape will four mice get? - Precisely 64114
We painted a wooden cube with an edge 4 cm long with green paint over the entire surface. Then we cut it into small cubes with an edge length of 1 cm. The number of cubes that have precisely two faces colored green is: - Perpendicular 5865
We cut the cube with two mutually perpendicular cuts, each parallel to one of the cube's walls. By what percentage is the sum of the surfaces of all cuboids created in this way greater than the surface of the original cube? - One dice
Calculate the probability of one dice roll with the numbers 1, 2, 3, 4, 5, and 6 on the walls. Write the results in a notebook in the shape of a fraction in the basic form: 2/3. a The number 1 falls on the cube. b, The number 5 falls on the cube. c, An ev - Multiply 6257
If we multiply the numbers of the last three pages of the book on pyramids, we get the product 23639616. How many pages does the book have if the last page's number is steam? - Opposite 79954
We color a wooden cube with an edge length of 3 cm so that three walls are blue, three are red, and no two opposite walls are the same color. Cut the cube into 1 cm³ cubes. How many cats will have at least one red wall and at least one blue wall? - Eiffel Tower
Eiffel Tower in Paris is 300 meters high and is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material if it weighs 2.4 kg? - Distribute 32451
The king cannot decide how to distribute 4 cubes of pure gold, which have edges of length 3cm, 4cm, 5cm, and 6cm, to two sons as fairly as possible. Design a solution so that the cubes do not have to be cut. - Z9-I-4
Kate thought of a five-digit integer. She wrote the sum of this number and its half in the first line of the workbook. On the second line, write a total of this number, and its one fifth. She wrote a sum of this number and its one nines on the third row. - Mouse Hryzka
Mouse Hryzka found 27 identical cubes of cheese. She first put a large cube out of them and then waited for a while before the cheese cubes stuck together. Then, she will eat the middle cube from every wall of the big cube. Then she also eats the cube in - Endless lego set
The endless lego set contains only 6, 9, and 20-kilogram blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And, of course, they wrote down how much the building weighed. - Shortest walk
An ant is crawling around this cube. The cube is made of wire. Each side of the cube is 3 inches long. (Those sides are called edges.) Points A and B are vertices of the cube. What is the least distance the ant would have to crawl if it starts from point - Ribbon on the cube
A cubical gift box is tied with a piece of ribbon. If the total length of the free ends and the bow is 18 inches, what is the length of the ribbon used? (Each side of the cube is 6 inches).
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