# Prime numbers + Mathematical Olympiad - math problems

#### Number of problems found: 12

- Year 2018

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

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