Mathematical Olympiad - practice for 11 year olds - last page
Number of problems found: 36
- Shopkeeper 4433
The seller of Christmas trees sold spruces for 220 CZK, pines for 250 CZK, and hemlocks for 330 CZK. In the morning he had an equal number of spruces, hemlocks, and pines. In the evening, he had sold all the trees and received a total of 36,000 CZK for th - Four families
Four families were on a joint trip. In the first family, there were three siblings: Alica, Betka, and Cyril. In the second family were four siblings: David, Erik, Filip, and Gabika. In the third family, there were two siblings, Hugo and Iveta. Three sibli - Centipede 4257
Centipede Mirka consists of a head and several articles. Each pair has one pair of legs. When it got cold, she decided to get dressed. Therefore, she put on a sock on her left foot in the third article from the end and then on every other third article. S - 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?
- Fluid
We have vessels containing 7 liters, 5 liters, and 2 liters. The largest container is filled with fluid, the others empty. Can you only get 5 liters and two 1 liter of fluid by pouring? How much pouring is needed? - 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 - Decide
The rectangle is divided into seven fields. On each box is to write just one of the numbers 1, 2, and 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 - 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 is true |DJ| - Soup
On Monday, we cook 25 pots and ten boilers of soup. On Tuesday, 15 pots and 13 boilers. On Wednesday, 20 pots and on Thursday, 30 boilers. On Monday and Tuesday was cooked the same amount of soup was. How many times is more soup cooked on Thursday than on
- Determine 2250
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 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 - Wipes
The mummy wiped out the square wipes, and the veil was next to each other on the cord stretched out between the two trees. She used a cord of 7.5 meters in length, requiring about 8 dm on each side of the trunk. All wipes are 45 cm wide. The mummy leaves - Square grid
A square grid consists of a square with sides of a length of 1 cm. Draw at least three patterns, each with an area of 6 cm² and a circumference of 12 cm, and their sides in a square grid.
- Number train
The numbers 1,2,3,4,5,6,7,8 and 9 traveled by train. The train had three cars, and each was carrying just three numbers. No. 1 rode in the first carriage, and in the last were all odd numbers. The conductor calculated the sum of the numbers in the first, - Pytagoriade
Two fifth-graders teams compete in math competitions - Mathematical Olympiad and Pytagoriade. Of the 33 students who competed in at least one of the contests, 22 students. Students who competed only in Pytagoriade were twice as many who just competed in t
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