Prime numbers - examples

  1. Dance ensemble
    dancers_1 The dance ensemble took the stage in pairs. During dancing, the dancers gradually formed groups of four, six and nine. How many dancers have an ensemble?
  2. Clock's gears
    orloj In the clock machine, three gears fit together. The largest has 168 teeth, the middle 90 teeth, and the smallest 48 teeth. The middle wheel turns around its axis in 90 seconds. How many times during the day do all the gears meet in the starting position?
  3. Inverted nine
    In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?
  4. Elevator
    age_3 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.
  5. PIN code
    pin_2 PIN on Michael credit card is a four-digit number. Michael told this to his friend: • It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself. • The first digit is larger than the second. • The second.
  6. Two buses
    bus27_14 The first bus runs 15 minutes the second bus runs after 21 minutes. Together they both leave at 7:00 on Monday. When and what day will they meet?
  7. Container
    cubes3_9 The container-shaped box with internal dimensions of 3.9 m, 3.25 m and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have?
  8. Minimum surface
    cuboid_20 Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
  9. Z9-I-4
    numbers_30 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. Fi
  10. No. of divisors
    triangle_div How many different divisors has number ??
  11. Numbers
    ten Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
  12. Meadow
    ovce-miestami-baran On the meadow grazing horses, cows and sheep, together 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 equall. How many horses, cows and sheep are on the meadow together?
  13. Cherries
    visne Cherries in the bowl can be divided equally among 8 or 10 or 11 children. How many is the minimum cherries in the bowl?
  14. Birthdate
    lizatka Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend?
  15. Mr. Zucchini
    cuketa Mr. Zucchini had a rectangular garden whose perimeter is 28 meters. Content area of the garden 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
  16. Plums
    svestka In the bowl are plums. How many would be there if we can divide it equally among 10, 12 and 14 children?
  17. Diofant 2
    1diofantos Is equation ? solvable on the set of integers Z?
  18. Plumber
    klempir Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it?
  19. Seedcake
    pletenky Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
  20. Diofant equation
    diofantos In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)

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