Mathematical Olympiad - practice problems - page 4 of 9
MO tasks are not easy, even for adults. At the same time, we believe that the right solution, which is here published almost on one click will serve as the inspiration.Do not be discouraged if you did not discover the right solution. Experiment, sketching, "play" with the problem. Sometimes it helps to look into a book and find out similar problems resolved. Sometimes help three days pause, and then you found the right solution.
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 162
- Single-digit 7302
Four different digits were on the four cards, one of which was zero. Vojta composed the largest four-digit number from the cards, and Martin the smallest four-digit number. Adam wrote the difference between Vojtov's and Martin's numbers on the board. Then - Parenthesis 7284 Tomas received nine cards with the following numbers and math symbols for math olympiad results. 18, 19, 20, 20, +, -, x, (,) Note 4 numbers and operators plus, minus, times, left parenthesis, right parenthesis. He stored the cards so that there were neve
- Year 2018
The product of the three positive numbers is 2018. What are the numbers? - Three-digit number
Find all three-digit numbers n with three different non-zero digits divisible by the sum of all three two-digit numbers we get when we delete one digit in the original number.
- Intersection 7247
On side AB of triangle ABC, points D and E are given such that |AD| = |DE| = |EB|. Points A and B are the midpoints of segments CF and CG. Line CD intersects line FB at point I, and line CE intersects line AG at point J. Prove that the intersection of lin - Quadrilaterals 7224
In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF parties are twice as long as the other parties. The lines BG and EL intersect at point M and divide the dode - Perpendicular 7223 In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF parties are twice as long as the other parties. The lines BG and EL intersect at point M. The quadrilateral
- Conditions 7186
Given an isosceles right triangle ABS with base AB. On a circle centered at point S and passing through points A and B, point C lies such that triangle ABC is isosceles. Determine how many points C satisfy the given conditions and construct all such point - Ticháček 7185
Mr. Ticháček had three gypsum dwarfs in the garden: the largest was called Maško, the middle Jarko, and the smallest Franko. Since he liked to play with them, he discovered that when he put Fan on Jarek, they were as tall as Maško. On the other hand, when
- Definitely 7179
Ivan and Mirka shared pears in the mission. Ivan always takes two pears, and Mirka takes half of what remains in the mission. Thus, Ivan, Mirka, Ivan, Mirka, and finally Ivan, who took the last two pears, took them away. Definitely. Who had more pears, in - MO C–I–1 2018 An unknown number is divisible by just four numbers from the set {6, 15, 20, 21, 70}. Determine which ones.
- Mathematical 7136 Out of 50 pupils, 44 solved at least one of the Olympiads - MO Mathematical Olympiad and BO Biology Olympiad. Twenty pupils still need to solve the MO. Of those who dealt with both Olympiads, 1/3 of those who dealt with just one were. How many pupils solv
- Bedrich and Adam
When Bedrich is as old as Adam today, Adam will be 14 years old. When Adam was as old as Bedrich, Bedrich was two years old today. How old are Adam and Bedrich today? - MO Z8-I-1 2018 Fero and David meet daily in the elevator. One morning, they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David.
- Together 7114
Michaella has five crayons. Victor has fewer of them than Michaella. Vendelín has as many as Michaella and Vojto have together. All three have seven times more crayons than Victor. How many crayons does Vendelín have? - Clubhouse
There were only chairs and tables in the clubhouse. Each chair had four legs, and the table was triple. Scouts came to the clubhouse. Everyone sat on their chair, two chairs were left unoccupied, and the number of legs in the room was 101. How many chairs - Interested 7090
We call a natural number N bombastic if it contains no zero in its notation and if no smaller natural number has the same product of digits as the number N. Charles first became interested in bombastic prime numbers and claimed that there were not many of - Sufficiently 7059
The king gave the mason Václav the task of building a wall 25 cm thick, 50 m long, and 2 m high. If Václav had worked without a break and at the same pace, he would have built a wall in 26 hours. However, according to the valid royal regulations, Wencesla - MO Z8–I–6 2018
The KLMN trapezium, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
Find all positive integers x and y for which: 1 / x + 1 / y = 1/4Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
