Mathematical Olympiad - math word problems - page 10 of 11
Number of problems found: 210
- Robots Z7
In the school for robots, one class is attended by twenty Robert robots, numbered Robert 1 to Robert 20. There is currently a tense atmosphere in the class, only some robots are talking to each other. Robots with an odd number do not talk with robots with - Next move MO
In the game renju, the starting player lays the first three stones (black, white, and black) on the intersections on the board, divided by 15 horizontal and 15 vertical lines, so that 225 intersections arise, observing the following rule: the first stone - Mr. Zucchini
Mr. Zucchini had a rectangular garden whose perimeter was 28 meters. The garden's area is filled with 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 - Decide
The rectangle is divided into seven fields. In each box, write just one of the numbers 1, 2, or 3. Mirek argues that it can be done so that the sum of the two numbers written next to each other is always different. Zuzana (Susan) instead argues that it is - Eight blocks
Dana had the task of saving the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be fo - Hexagon - MO
The picture shows the ABCD square, the EFGD square, and the HIJD rectangle. Points J and G lie on the side CD and are true |DJ| - MO 2016 Numerical axis
Cat's school uses a special numerical axis. The distance between the numbers 1 and 2 is 1 cm, the distance between the numbers 2 and 3 is 3 cm, between the numbers 3 and 4 is 5 cm, and so on, and the distance between the next pair of natural numbers is al - Archaeologists
Archaeologists found out that the flag of the fabled mathematical kingdom was divided into six fields, as shown in the picture. In reality the flag was tri-coloured and each field was coloured with one colour. The scientists have already discovered that o - Internal angles
The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On the BC side is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA, the point M is such that | DM | = 2 |MA|. Det - Hexagons
There is a square ABCD, a square EFGD, and a rectangle HIJD. Points J and G lie on side CD, with DJ less than DG, and points H and E lie on side DA, with DH less than DE. We also know that DJ equals GC. Hexagon ABCGFE has a perimeter of 96 cm, hexagon EFG - Soup
On Monday, we cooked 25 pots and ten boilers of soup. On Tuesday, we cooked 15 pots and 13 boilers. On Wednesday, we cooked 20 pots, and on Thursday, we cooked 30 boilers. The same amount of soup was cooked on Monday and Tuesday. How many times is more so - MO - triangles
On the AB and AC sides of the ABC triangle lies successive points E and F, and on segment EF lie point D. The EF and BC lines are parallel. It is true this ratio FD:DE = AE:EB = 2:1. The area of the ABC triangle is 27 hectares, and line segments EF, AD, a - Keyboards keys
Michael had small keys on the shelf, which you can see in the picture. Their tones were marked on the white keys. Little Clara found the keys. As she took them off the shelf, they fell out of her hand, and all the white keys spilled out. So that the broth - Katy MO
Kate drew a triangle ABC. The middle of the line segment AB is marked as X, and the center of the side AC is marked as Y. On the side BC, she wants to find point Z so that the area of a 4gon AXZY is the greatest. What part of the ABC triangle can maximall - Day Number
The day number is the serial number of the day in the relevant month (i.e., the number on 5 August 2016 is 5). The digit sum of the day is the sum of the values of all digits on the date of that day (i.e., the digit sum on 5 August 2016 is 5 + 8 + 2 + 0 + - Chamber
In the chamber, light is broken, and all from it must be taken at random. Socks have four different colors. If you want to be sure of pulling at least two white socks, we have to bring them out 28 from the chamber. To have such certainty for the pair of g - Mouse Hryzka
Mouse Nibbles 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 - Pentagon
Within a regular pentagon ABCDE point, P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch. - Meadow
On the meadow, there are horses, cows, and sheep grazing together with less than 200. If cows were 45 times more, horses 60 times more, and sheep 35 times more than there are now, their numbers would equal. How many horses, cows, and sheep are in the mead - Exchange rate - currency
The exchange rate list in the table is an exchange office, but question marks replace some values. The exchange office exchanges money at the rates quoted and does not charge any other fees. nákup prodej 1 EUR 26,20 CZK 28,00 CZK 1 GBP b=? CZK c=? CZK 1.
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