Mathematical Olympiad - practice problems - page 8 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
- 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 - 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 - 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 - 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
- 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 - Exchanged 2214
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. - MO circles
Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle with a center at point B passing through point A and a semicircle l with a center at the center of the BC side and passed point B. He would still build a circle th - TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have
- Amazing number
An amazing number is a name for such an even number, the decomposition product of prime numbers has exactly three, not necessarily different factors, and the sum of all its divisors is equal to twice that number. Find all the amazing numbers. - 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, - Christmas Day
In leap years, it was 53 Sundays. On what day of the week fell Christmas Day?
When lord Ram was founded, the breed of white sheep was eight more than black. White sheep are four times higher than at the beginning, and black three times more than at the beginning. White sheep is now 42 more than the black. How many white and black sDo you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
