The most difficult problems

Number of problems found: 6044

  • Right triangle from axes
    axes2 A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
  • Reciprocal equation 2
    parabola2 Solve this equation: x + 5/x - 6 = 4/11
  • Prime factors
    prime Write 98 as product of prime factors
  • Isosceles
    rr_lichobeznik_1 Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
  • Rectangles
    rectangles2_3 How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm? (a rectangle with sides of 50cm and 450cm is considered to be the same as a rectangle with sides of 450cm and 50cm)
  • Square into three rectangles
    stvorcove-cisla_1 Divide the square with a side length of 12 cm into three rectangles with have the same circumference so that these circumferences are as small as possible.
  • Right triangle
    rt_A Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
  • Sandbox
    sand_2 Sandbox has area of 32 sq ft and length of 4 1/2 ft. What is width of sandbox.
  • 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.
  • Geometric progression 4
    square_rot_1 8,4√2,4,2√2
  • Algebra
    parabol_3 X+y=5, find xy (find the product of x and y if x+y = 5)
  • Simplify 3
    fractal_14 Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
  • Adding mixed numerals
    zlomky_18 3 3/4 + 2 3/5 + 5 1/2 Show your solution.
  • Lampshade
    kuzel_2 The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm2 of material will we need when we 10% is waste?
  • 15 teachers
    skola_13 15 teachers teach for a combined amount of 128 days over a period of 64 days. What is this expressed as a percentage?
  • 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?
  • A man
    penize_49 A man spends 5/9 of his money on rent, and 5/16 of the remainder on electricity. If the final balance remaining is 550 find how much was spent on rent
  • Cube, cuboid, and sphere
    cubes3_8 Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. At what rate are the volumes of cube, cuboid, and sphere?
  • Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  • Taxi
    linear_eq_1 A taxi ride costs $3 plus $2.50 per mile. Write and Graph an equation in two variables that represents the total cost of a taxi ride.

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...