The most difficult problems

Number of problems found: 7295

  • Sum of two primes
    prime Christian Goldbach, a mathematician, found out that every even number greater than 2 can be expressed as a sum of two prime numbers. Write or express 2018 as a sum of two prime numbers.
  • Population growth
    exp_growth How many people will be on Earth from two people for 5,000 years, if every couple has always 4 children, (2 boys and 2 girls) at the age of 25-35, and every man will live 75 years?
  • Butter
    factory_butter At the Orville redenbocher popcorn factory there is a tank of artificial butter substitute which is 55 feet tall and 18 feet in diameter. How many gallons of artificial butter substitute can the tank contain?
  • 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 a product of prime factors
  • Isosceles
    rr_lichobeznik Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
  • Rectangles
    rectangles2 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 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.
  • Sandbox
    sand Sandbox has area of 32 sq ft and length of 4 1/2 ft. What is width of sandbox.
  • Digits
    seq 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 8,4√2,4,2√2
  • Algebra
    parabol If x+y=5, find xy (find the product of x and y if x+y = 5)
  • Simplify 3
    fractal Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
  • Adding mixed numerals
    zlomky 3 3/4 + 2 3/5 + 5 1/2 Show your solution.
  • Lampshade
    kuzel 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 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 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?
  • Cube, cuboid, and sphere
    cubes3.png 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 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3

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