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.

Number of problems found: 64

  • Pytagoriade
    pytagoriada Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just compete
  • Christmas Day
    stedryd In leap years was 53 Sundays. On what day of the week fell to Christmas Day?
  • 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.
  • Year 2018
    new_year The product of the three positive numbers is 2018. What are the numbers?
  • Decide
    mo_1 The rectangle is divided into seven fields. On each box is to write just one of the numbers 1, 2 and 3. Mirek argue that it can be done so that the sum of the two numbers written next to each other was always different. Zuzana (Susan) instead argue that i
  • 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?
  • 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.
  • 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 ∗ ∗
  • 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?
  • 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.
  • Twos
    2019 Vojta started writing the number of this year 2019202020192020 into the workbook. .. And so he kept going. When he wrote 2020 digits, no longer enjoyed it. How many twos did he write?
  • Star equation
    numbers_37 Write digits instead of stars so that the sum of the written digits is odd and is true equality: 42 · ∗8 = 2 ∗∗∗
  • Last digit
    olympics_3 What is the last number of 2016 power of 2017
  • 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|
  • 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.
  • 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?
  • Skiing meeting
    compass4 On the skiing meeting came four friends from 4 world directions and led the next interview. Charles: "I did not come from the north or from the south." Mojmir "But I came from the south." Joseph: "I came from the north." Zdeno: "I come from the south." We
  • 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 . ..
  • 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.
  • 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

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...



See also more information on Wikipedia.