Mathematical Olympiad - practice problems - page 7 of 9
MO tasks are not easy, even for adults. At the same time, we believe that the right solution, which is here published almost on one click will serve as the inspiration.Do not be discouraged if you did not discover the right solution. Experiment, sketching, "play" with the problem. Sometimes it helps to look into a book and find out similar problems resolved. Sometimes help three days pause, and then you found the right solution.
Number of problems found: 162
- Christmas trees
The salesman sold Christmas trees: spruce for € 22, pine for € 25, and fir for € 33. In the morning, he had the same number of spruce, fir, and pine. In the evening, he had all the trees sold for € 3,600. How many trees does the day salesman sell? - MO-Z5-3-66 tiles
The picture shows square tiles with a side of 10 dm, composed of four identical small rectangles and squares. The circumference of a small square is five times smaller than the circumference of the entire tile. Determine the dimensions of the rectangle. - Candy - MO
Gretel deploys different numbers to the vertex of a regular octagon, from one to eight candy. Peter can then choose which three piles of candy to give Gretel others retain. The only requirement is that the three piles lie at the vertices of an isosceles t - Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7, and 8, wherein on different sides are different numbers. John makes the sum of the numbers written on three adjacent walls for each wall. Thus got eight sums, which al
- Three friends
Three friend squirrels together went to collect hazelnuts. Zrzecka found more than twice Pizizubka, and Ouska was even three times more than Pizizubka. On the way home, they talked while eating and cracked her nuts. Pizizubka ate half of all the nuts coll - Z9–I–1
All nine fields of given shape are to be filled with natural numbers so that: • each of the numbers 2, 4, 6, and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in t - Mrak - cloud
It is given segment AB, which is 12 cm in length, on which one side of the square MRAK is laid. MRAK's side length is 2 cm shown. MRAK gradually flips along the line segment AB, and point R leaves a paper trail. Draw the whole track of point R until the s - Abbreviation 4148
From point A to point C, an educational trail passes through point B and a red tourist sign; see the picture. In addition, an undrawn abbreviation 1500 meters long, starting at A and ending on the nature trail, can be used. Vojtech found that • the trip f - MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and swam in the water. Its highest point was 2 cm above the surface. The circle's diameter that marked the water level on the ball's surface was 8 cm. Find the diameter of John's ball.
- Skiing meeting
Four friends came to the skiing meeting from 4 world directions and led the next interview. Charles: "I did not come from the north or from the south." Mojmir: "But I came from the south." Joseph: "I came from the north." Zdeno: "I come from the south." W - 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. Write a total of this number and its fifth on the second line. She wrote a sum of this number and its one nines on the third row. Finall - Tunnels
Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber, mice can get to an - Fluid
We have vessels containing 7 liters, 5 liters, and 2 liters. The largest container is filled with fluid, and the others are empty. Can you only get 5 liters and two 1 liter of fluid by pouring? How much pouring is needed? - Pet store
They sold fish from one aquarium from the breeding product (Zverimex). Ondrej wanted half of all the fish, but to avoid cutting any fish, he got half the fish more than he wanted. Matej wanted half of the remaining fish, but like Ondrej, he got half the f
- Connected 3457
There are eight places in Budan, some of which are connected by roads. There is a gate at every point where the road leaves or enters the city. No two paths intersect or enter through the same entrance. The number of gates matches one of the numbers 5,15, - Rectangular 2885
A total of ten exhibitors gathered at the long-haired cat show. It was exhibited in a rectangular room with two rows of tables, as shown. The cats were marked with different numbers from 1 to 10, and one cat sat on each table. Determine which cat was rate - 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
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|Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
