Maximum + minimum - math problems

Number of problems found: 25

  • Camp
    tabor In a class are 26 children. During the holidays 16 children were in the camps and 14 children on holiday with their parents. Determine the minimum and maximum number of children that may have been in the camp and on holiday with their parents at the same
  • Statue
    michelangelo On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
  • Cone
    diag22 Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
  • Digits
    numbers_2 Write the smallest and largest 2-digit number.
  • Glasses
    class Imagine a set of students in your class (number of students: 19), who wears glasses. How much minimum and maximum element may contain this set.
  • Classmates
    meter_13 Roman is ranked 12th highest and eleventh lowest pupil. How many classmates does Roman have?
  • Trousers
    venn_diagram In the class was 12 students. Nine students wearing trousers and turtleneck eight. How many students worn trousers with a turtleneck?
  • Shape
    some_airplane Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
  • Skoda cars
    car_11 There were 16 passenger cars in the parking. It was the 10 blue and 10 Skoda cars. How many are blue Skoda cars in the parking?
  • Ladder
    rebrik_4 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
  • Curve and line
    parabol The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
  • Cylindrical container
    valec2_6 An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
  • Derivative problem
    derive The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive and the product of one with the other power of the other is maximal.
  • Bouquet
    flowers_1 Gardener tying bouquet of flowers for 8 and none was left. Then he found that he could tying bouquet of 6 flowers and also none was left. How many have gardener flowers (minimum and maximum) if they had between 50 and 100 flowers?
  • Ten boys
    venn_intersect Ten boys chose to go to the supermarket. Six boys bought gum and nine boys bought a lollipop. How many boys bought gum and a lollipop?
  • Cookies
    poleva In the box were total of 200 cookies. These products have sugar and chocolate topping. Chocolate topping is used on 157 cookies. Sugar topping is used on 100 cakes. How many of these cookies has two frosting?
  • The shooter
    terc The shooter shoots at the target, assuming that the individual shots are independent of each other and the probability of hitting each of them is 0.2. The shooter fires until he hits the target for the first time, then stop firing. (a) What is the most li
  • Paper box
    box Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box?
  • 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
  • Secret treasure
    max_cylinder_pyramid Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...