Natural numbers - examples

  1. Sum of inner angles
    angle-sum-of-polygon Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
  2. Digits
    seq_5 Show that if x, y, z are 3 consecutive nonzero digits, zyx-xyz = 198, where zyx and xyz are three-digit numbers created from x, y, z.
  3. Rectangles
    rectangle_15 The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
  4. Three friends
    gulky_9 Three friends had balls in ratio 2: 7: 4 at the start of the game. Could they have the same number of balls at the end of the game? Write 0, if not, or write the minimum number of balls they had together.
  5. Brick
    brick One brick is 6 kg and half a brick heavy. What is the weight of one brick?
  6. Chocolate
    cokolada Juan bought 9 same chocolates for 9 Eur. How many euros he pay for 29 chocolates?
  7. Divisibility
    divisibility Is the number 146025 divisible by 6?
  8. Monkey
    monkey Monkey fell in 38 m deep well. Every day her scramble 3 meters, at night dropped back by 2 m. On that day it gets hangover from the well?
  9. Diophantus
    diofantos_1 We know little about this Greek mathematician from Alexandria, except that he lived around 3rd century A.D. Thanks to an admirer of his, who described his life by means of an algebraic riddle, we know at least something about his life. Diophantus's youth l
  10. 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
  11. No. of divisors
    triangle_div How many different divisors has number ??
  12. Textbooks
    textbooks After check of textbooks found that every 10-th textbook should be withdrawn. Together 58 textbooks were withdrawn. How many textbooks were in stock before withdrawn and how many after withdrawn?
  13. Numbers
    ten Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
  14. Steps
    square_diagonal_1 How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 307 steps.
  15. Weeks
    calendar 33 weeks is equal to how many days?
  16. Z9–I–1
    ctverec_mo In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir
  17. 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?
  18. Camp
    skauti In the camp are children. 1/2 went on a trip, 1/4 went to bathe and 58 children remained in the room. How many children are in camp?
  19. Balls
    balls I have 19 balls and my friend has 27. About how many has my friend more balls?
  20. 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?

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