# Mathematical Olympiad + divisibility - practice problems

#### Number of problems found: 14

- Coloured numbers

Mussel wrote four different natural numbers with coloured markers: red, blue, green and yellow. When the red number divides by blue, it gets the green number as an incomplete proportion, and yellow represents the remainder after this division. When it div - 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. - Twos

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? - 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? - Year 2018

The product of the three positive numbers is 2018. What are the numbers? - 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. - Z9–I–4 MO 2017

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 - 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. - Z9-I-4

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. Fina - Fluid

We have vessels containing 7 liters, 5 liters, and 2 liters. The largest container is filled with fluid, the others empty. Can you only by pouring get 5 liters and two 1 liter of fluid? How much pouring is needed? - Pet store

In a pet store, they are selling out the fish from one aquarium. Ondra wanted half of all fish, but they don't wish cut by hal fany fish he got one more than demanded. Matthew wished the remaining half of the fish, but as Andrew got half the fish more tha - 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 - Meadow

On the meadow grazing horses, cows, and sheep, together with 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 equally. How many horses, cows, and sheep are on the meadow toget - Amazing number

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.

We apologize, but in this category are not a lot of examples.

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Mathematical Olympiad - practice problems. Divisibility - practice problems.