The most difficult problems
Number of problems found: 7295
- 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 a product of prime factors
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.
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
If 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.
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
15 teachers teach for a combined amount of 128 days over a period of 64 days. What is this expressed as a percentage?
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
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
If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3