Mathematical Olympiad - practice problems - page 9 of 11
Number of problems found: 210
- Carillon MO - Z5 - 1 - 66
The carillon in the courtyard plays at every full hour a short composition, starting at 8 a.m. and ending at 10 p.m. The compositions total eighteen, at the full hour always only one is played, and after playing all eighteen it starts again in the same or - 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. - Take a photo
Four boys live in a three-story house. Each lives on a different floor. We know the following about them: - Josef is a philatelist. - Viktor does not live on the top floor and is not a photographer. - Ivan is friends with an amateur photographer who lives - Z6–I–2
Mr. Kockorád owned a rectangular-shaped garden, on which he gradually paved paths from one side to the other. The paths were equally wide, crossed each other at two places, and the already paved area was skipped when paving further. When Mr. Kockorád pave - 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 - Educational trails
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. Victor found that • the trip fr - MO SK/CZ Z9–I–3
John had a ball that rolled into a pool and floated on the water. Its highest point was 2 cm above the surface. The diameter of the circle where the ball met the water 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 ninth on the third row. Finall - Tunnels
Mice built an underground house consisting of chambers and tunnels: • every tunnel connects one chamber to another (no dead ends), • exactly three tunnels lead from each chamber to three distinct other chambers, • from every chamber, a mouse can reach any - 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). Andrew wanted half of all the fish, but to avoid cutting any fish, he got half the fish more than he wanted. Matthew wanted half of the remaining fish, but like Andrew, he got half the - City gates
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, - Ships
1. The Greek ship leaves at 6 and carries coffee. 2. The middle ship has a black chimney. 3. The English ship leaves at nine. 4. The French ship is to the left of the ship that carries coffee and has a blue chimney. 5. To the right of the ship carrying co - Cat show
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
Do you have unsolved math question and you need help? Ask a question, and we will try to solve it. We solve math question.
