Mathematical Olympiad - math word problems

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 not discovered 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 right solution.

  1. TV transmitter
    praded 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.
  2. Z9-I-4
    numbers_30 Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi
  3. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
  4. Chamber
    socks 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. In order to have such certainty for the pai
  5. Meadow
    ovce-miestami-baran On the meadow grazing horses, cows and sheep, together 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 equall. How many horses, cows and sheep are on the meadow together?
  6. Z9–I–1
    ctverec_mo In all nine fields of given shape to be filled 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 the cir
  7. Mr. Zucchini
    cuketa Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. Content area of the garden 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
  8. Octahedron - sum
    8sten 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. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
  9. Pentagon
    5gon_1 Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
  10. Square grid
    sit Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.
  11. Hexagon - MO
    6uholnik_nepravidelny 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|
  12. MO - triangles
    metal On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB se
  13. Amazing number
    numbers4 An amazing number is name for such 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 amazing numbers.
  14. Christmas Day
    stedryd In leap years was 53 Sundays. On what day of the week fell to Christmas Day?
  15. Mouse Hryzka
    myska_hryzka Mouse Hryzka found 27 identical cubes of cheese. She first put in a large cube out of them and then waited for a while before the cheese cubes stuck together. Then from every wall of the big cube she will eats the middle cube. Then she also eats the cube
  16. Lord Ram
    sheep When lord Ram founded the breed white sheep was 8 more than black. Currently 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 sh
  17. MO circles
    mo Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle that had a center at point B passing through point A and a semicircle l that had a center at the center of the BC side and passed point B. He would still build a ci
  18. Trapezoid MO-5-Z8
    lichobeznik_mo_z8 ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
  19. Number train
    train2 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 carriage was all odd numbers. The conductor calculated sum of the numbers in the first
  20. Internal angles
    mo-klm The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC 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|. Dete

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