Reason + Mathematical Olympiad - examples

  1. Year 2018
    new_year The product of the three positive numbers is 2018. What are the numbers?
  2. MO C–I–1 2018
    numbers_49 An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
  3. MO Z8-I-1 2018
    age_6 Fero and David meet daily in the elevator. One morning they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
  4. 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
  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. 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
  7. 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
  8. 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
  9. 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.
  10. Christmas Day
    stedryd In leap years was 53 Sundays. On what day of the week fell to Christmas Day?
  11. 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
  12. 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
  13. 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
  14. 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
  15. Tunnels
    Mysky 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 any
  16. Eight blocks
    cuboids Dana had the task to save 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 four
  17. Bicycles
    cyclist_11 You're the owner of the transport 's learning playground. Buy bicycles of two colors but you've got to spend accurately 120000 Kč. Blue bike costs 3600Kč and red bicycle 3200Kč.
  18. Fluid
    nadoby We have vessels containing 7 liters, 5 liters and 2 liters. Largest container is filled with fluid the others empty. Can you only by pouring get 5 liters and two 1 liter of fluid? How many pouring is needed?
  19. MO-Z5-3-66 tiles
    stvorce The picture shows a square tiles with side 10 dm which is composed of four identical small rectangles and squares. Circumference of small square is five times smaller than the circumference of the entire tile. Determine the dimensions of the rectangle.
  20. Cakes Z8-I-5
    cukriky_5 Mom brought 10 cakes of three types: kokosek was less than laskonek and most were caramel cubes. John chose two different kinds of cakes, Stephan did the same and for Margerith leave only the cakes of the same type. How many kokosek, laskonek and caramel c

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