# 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? - 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

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

Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area. - Rectangles

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

Sandbox has area of 32 sq ft and length of 4 1/2 ft. What is width of sandbox. - Digits

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

8,4√2,4,2√2 - Algebra

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. - Lampshade

The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm^{2}of material will we need when we 10% is waste?

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