The most difficult problems

  1. Possible combinations - word
    dices2 How many ways can the letters F, A, I, R be arranged?
  2. Two divided
    fractions14 Two divided by nine tenths.
  3. Tenths digit
    numbers2 For 10.932, which digit is in the tenths place?
  4. Two dogs
    calendar Izzy's dog is 10 1/2 years old. Paige's dog is 18 months old. How many years older is Izzy's dog?
  5. Conical bottle
    cone-upside When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
  6. Weigh in total
    box I put 3/5kg of grapes into a box which is 1/4kg in weight. How many kilograms do the grapes and the box weigh in total?
  7. Two bodies
    cylinders The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Determine the ratio of surfaces of the first and seco
  8. Two accounts
    bank A banker divided $5000 between 2 accounts, one paying 10% annual interest and the second paying 8% annual interest. Express the amount invested in the 10% account in the terms of the amount invested in the 8% account.
  9. The percent 2
    penize The percent return rate of a growth fund, income fund, and money market are 10%, 7%, and 5% respectively. Suppose you have 3200 to invest and you want to put twice as much in the growth fund as in the money market to maximize your return. How should you i
  10. Five harvests
    zrno In the seed company, they know that, out of 100 grains of a new variety, they get an average of 2000 grains after harvest. Approximately how many grains do they get out of 100 grains after five harvests?
  11. Diagonal intersect
    rrLichobeznik isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles?
  12. One third power
    cube-root Which equation justifies why ten to the one-third power equals the cube root of ten?
  13. College 2
    fuel College student is moving into a dormitory. The student rent a truck for $19.95 plus $0.99 per mile. Before returning the truck the student fills the tank with gasoline, which cost $65.32. Total cost $144.67. Using a linear equation, explain the process t
  14. The Indian tent
    indian_stan The Indian tent is cone-shaped. Its height is 3.5 m. The diameter of the base is 2.5 m. How much canvas is needed to make a tire?
  15. Parallel and orthogonal
    vectors2 I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w
  16. Bisectors
    right_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
  17. Surface area of a cube
    cube_shield What is the surface area of a cube that has an edge of 3.5?
  18. Regular hexagonal pyramid
    hexa_pyramid Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture.
  19. Octagonal pyramid
    octagonl_pyramid2 Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
  20. Tetrahedral pyramid
    ihlan Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, 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...