# Reason + Mathematical Olympiad - math problems

#### Number of problems found: 44

- Year 2018

The product of the three positive numbers is 2018. What are the numbers? - Christmas Day

In leap years was 53 Sundays. On what day of the week fell to Christmas Day? - Pytagoriade

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 - MO C–I–1 2018

An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones. - Twos

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? - All pairs

Determine all pairs (m, n) of natural numbers for which is true: m s (n) = n s (m) = 70, where s (a) denotes the digit sum of the natural number a. - Six-digit primes

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? - Star equation

Write digits instead of stars so that the sum of the written digits is odd and is true equality: 42 · ∗8 = 2 ∗∗∗ - MO Z6-6-1

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? - Z7-I-4 stars 4949

Write instead of stars digits so the next write of product of the two numbers to be valid: ∗ ∗ ∗ · ∗ ∗ ∗ ∗ ∗ ∗ ∗ 4 9 4 9 ∗ ∗ ∗ ∗ ∗ ∗ 4 ∗ ∗ - Pyramid Z8–I–6

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

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 - Alarm clock

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 . .. - Last digit

What is the last number of 2016 power of 2017 - Bicycles

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. - Fluid

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? - Average age

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? - MO-Z5-3-66 tiles

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. - Mr. Zucchini

Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. The garden's content area 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 - Skiing meeting

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

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