The most difficult problems
Number of problems found: 5745
- Sum of two primes
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
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?
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
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
Solve this equation: x + 5/x - 6 = 4/11
- Prime factors
Write 98 as product of prime factors
- Paper box
Calculate how much we'll pay for a three-side shaped prism box with a triangular base, and if it measures 12cm and 1.6dm, the hypotenuse measures 200mm. The box is 34cm high. We pay 0,13 € per square meter of paper.
Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.
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
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
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 has area of 32 sq ft and length of 4 1/2 ft. What is width of sandbox.
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
X+y=5, find xy (find the product of x and y if x+y = 5)
- Simplify 3
Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
- Adding mixed numerals
3 3/4 + 2 3/5 + 5 1/2 Show your solution.
- Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
- An oil
An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters.
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?