Integers + natural numbers - examples

  1. Divisibility
    divisibility Is the number 761082 exactly divisible by 9? (the result is the integer and/or remainder is zero)
  2. Monkey
    monkey Monkey fell in 23 meters deep well. Every day it climbs 3 meters, at night it dropped back by 2 m. On what day it gets out from the well?
  3. Diofant 2
    1diofantos Is equation ? solvable on the set of integers Z?
  4. 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)
  5. Mistake
    minus Nicol mistake when calculate in school. Instead of add number 20 subtract it. What is the difference between the result and the right result?
  6. Class
    pytagoras_class When Pythagoras asked how many students attend the school, said: "Half of the students studying mathematics, 1/4 music, seventh silent and there are three girls at school." How many students had Pythagoras at school?
  7. Rectangle
    rectangles_1 The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
  8. Line
    negative_slope Straight line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line which both coordinates are positive integers.
  9. Gauss
    kfgauss Help little C.F. Gauss sum all the integers from 1 to 400.
  10. Remainders
    dividing It is given a set of numbers { 170; 244; 299; 333; 351; 391; 423; 644 }. Divide this numbers by number 66 and determine set of remainders. As result write sum of this remainders.
  11. Integers
    calculator_mechanical May be the sum of two integers less than their difference?
  12. CZK coins
    CZK-coins Thaddeus and Jolana together have 15 CZK. Jolana has half of Thaddeus money. Nevertheless Jolana has 3 coins and Thaddeus 2 coins. Which coin has Thaddeus and Jolana (Help: CZK coins has values 1,2,5,10,20,50 CZK)?
  13. Legs
    zidle In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people?
  14. Clotheslines
    snura Mommy needs 6 clothesline 360 cm long. Clotheslines is sold in the length of eight meters. How many of these clotheslines must buy mom if any does not want to be connected? How much mommy pay for the clotheslines when 1 piece costs 24kč?
  15. Four integers
    tiles2 Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
  16. Modulo
    modulo Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .
  17. One hundred stamps
    stamp_4 A hundred letter stamps cost a hundred crowns. Its costs are four levels - twenty tenths , one crown, two-crown and five-crown. How many are each type of stamps? How many does the problem have solutions?
  18. Endless lego set
    lego_2 The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. They
  19. Candy and boxes
    cukriky_13 We have some number of candy and empty boxes. When we put candies in boxes of ten, there will be 2 candies and 8 empty boxes left, when of eight, there will be 6 candies and 3 boxes left. How many candy and empty boxes left when we put candies in boxes of.
  20. Triangles
    496_triangle Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm and the length of the third side is expressed in whole centimeters. How many triangles does he have?

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