# 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?
• 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 a product of prime factors
• 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.
• 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 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. 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?
• Rectangles 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

Do you have an exciting math question or word problem that you can't solve? Ask a question or post 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...