Square + divisibility - practice problems
Number of problems found: 24
- Asymmetric 5407
Find the smallest natural number k for which the number 11 on k is asymmetric. (e.g. 11² = 121) - Directly 55591
If n is a natural number that gives a division of 2 or 3 when divided by 5, then n gives a residue of 4 when divided by 5. Prove directly - Rectangles
How many rectangles with area 3152 cm² whose sides are natural numbers? - Probability 17013
What is the probability that a randomly written two-digit number from number 20 to number 99 will be divisible by 11, the power of number 3, or a prime number? - Square room
What is the size of the smallest square room, which can be paved with tiles with dimensions of 55 cm and 45 cm? How many such tiles are needed? - Three-digit 5312
Find the smallest four-digit number abcd such that the difference (ab)²− (cd)² is a three-digit number written in three identical digits. - Trams 2
Square passes two lines of the tram. One is running every nine minutes, the second interval of 15 minutes. Exactly at noon arrived two tram lines in the square. How soon should a similar situation arise again? - Expression 4451
Find the largest natural number d that has that property for any natural number the number n is the value of the expression V (n) = n ^ 4 + 11n²−12 is divisible by d. - Maximally 4036
Mr. Novák wants to pave the terrace with tiles of two sizes to be as small as possible. Its terrace is square with a side 3 meters long. There is a wall of the house on two sides of the terrace. Next to the wall, he wants to put small tiles, the rest larg - Tiles
From how many tiles, 20 cm by 30 cm, we can build a square of maximum dimensions if we have maximum 275 tiles. - Measuring 26891
What is the smallest square space we can tile with tiles measuring 25 x 15 cm, knowing there will be no need to cut them? How many tiles will we use? - Diophantus
We know little about this Greek mathematician from Alexandria, except that he lived around the 3rd century A. D. Thanks to an admirer of his, who described his life through an algebraic riddle, we know at least something about his life. Diophantus's youth - Plumber
The plumber had to cut the metal strip with dimensions of 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it? - Mr. Zucchini
Mr. Zucchini had a rectangular garden whose perimeter was 28 meters. The garden's area filled just four square beds, whose dimensions in meters are expressed in whole numbers. Determine what size could have a garden. Find all the possibilities and write n - Tiles
Hall has dimensions 250 × 200 dm. What is the largest size of square tiles that can be entire hall tiled, and how many do we need them? - Rectangular 56801
We are to create a square in the shape of a rectangle with an area of 288 m² (square) so that the sides are whole numbers. What are all the dimensions of the rectangular box we can make? How many is the solution? - Tiles
The room has dimensions of 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover the room's floor. - Paper squares
We should cut the paper rectangle measuring 69 cm and 46 cm into as many squares as possible. Calculate the lengths of squares and their number. - Tiles
The tile has the shape of a square with a side of 15 cm. What dimensions can a rectangle composed of 90 tiles have so that no tile remains? - Bricks pyramid
How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
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