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 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.

  1. Twos
    2019 Vojta started writing the number of this year 2019202020192020 into the workbook. . And so he kept going. When he wrote 2020 digits, he no longer enjoyed it. How many twos did he write?
  2. Between two bus stops
    bus27 Wanda lives between two bus stops at three-eighths of their distance. He started the house today and found that whether he was running to one or the other stop, he would have arrived at the bus stop. The average bus speed is 60 km/h. What is the average
  3. Luggage and air travel
    aircraft-02_14 Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have, how many kilograms of lugg
  4. Six-digit primes
    numberline_1 Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they?
  5. Year 2018
    new_year The product of the three positive numbers is 2018. What are the numbers?
  6. 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.
  7. 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.
  8. Clubhouse
    stol_2 There were only chairs and table in the clubhouse. Each chair had four legs, and the table was triple. Scouts came to the clubhouse. Everyone sat on their chair, two chairs were left unoccupied, and the number of legs in the room was 101. How many chairs w
  9. MO Z8–I–6 2018
    lich_1 In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
  10. Equilateral triangle ABC
    equliateral In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
  11. Last digit
    olympics_3 What is the last number of 2016 power of 2017
  12. Z9–I–4 MO 2017
    vlak2 Numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of each of the three was equal to the sum of the remaining two. The conduct
  13. Average age
    age_4 The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?
  14. MO8-Z8-I-5 2017
    mo8 Identical rectangles ABCD and EFGH are positioned such that their sides are parallel to the same. The points I, J, K, L, M and N are the intersections of the extended sides, as shown. The area of the BNHM rectangle is 12 cm2, the rectangle MBCK area is 63.
  15. One million
    million Write the million number (1000000) by using only 9 numbers and algebraic operations plus, minus, times, divided, powers, and squares. Find at least three different solutions.
  16. Alarm clock
    clock-night-schr The old watchmaker has a unique digital alarm in its collection that rings whenever the sum of digits of the alarm is equal to 21. Find out when the alarm clock will ring. What is their number? List all options . ..
  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. MO Z6-6-1
    kruhy_1 Write integers greater than 1 to the blanks in the following figure, so that each darker box was product of the numbers in the neighboring lighter boxes. What number is in the middle box?
  19. Z7-I-4 stars 4949
    hviezdicky_mo Write instead of stars digits so the next write of product of the two numbers to be valid: ∗ ∗ ∗ · ∗ ∗ ∗ ∗ ∗ ∗ ∗ 4 9 4 9 ∗ ∗ ∗ ∗ ∗ ∗ 4 ∗ ∗
  20. Pyramid Z8–I–6
    pyramida_mo Each brick of pyramid contains one number. Whenever possible, the number in each brick is lowest common multiple of two numbers of bricks lying directly above it. That number may be in the lowest brick? Determine all possibilities.

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