Mathematical Olympiad + sets - practice problems
Number of problems found: 9
- Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400? - Construct 11511
Construct the diamond ABCD so that its diagonal BD is 8 cm and the distance of apex B from the line AD is 5 cm. Specify all options - Four-digit 10261
Roman likes magic and math. Last time he conjured three- or four-digit numbers like this: • created two new numbers from the given number by dividing it between digits in the place of hundreds and tens (e.g., from the number 581, he would get 5 and 81), • - Sufficient 9391
In Kocourkov, they use coins with only two values expressed in Kocourkov crowns by positive integers. With a sufficient number of such coins, it is possible to pay any integer amount greater than 53 cats’ crowns accurately and without return. However, we - Justification 8468
The natural number n has at least 73 two-digit divisors. Prove that one of them is the number 60. Also, give an example of the number n, which has exactly 73 double-digit divisors, including a proper justification. - 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 - Participants 5319
In the mathematical competition, its participants solved two tasks. Everyone solved at least one problem, while 80% of the participants solved the first problem, and 50% solved the second problem. Sixty participants solved both tasks. How many participant - Chamber
In the chamber, light is broken, and all from it must be taken at random. Socks have four different colors. If you want to be sure of pulling at least two white socks, we have to bring them out 28 from the chamber. To have such certainty for the pair of g - Pytagoriade
Two fifth-graders teams compete in math competitions - Mathematical Olympiad and Pytagoriade. Of the 33 students who competed in at least one of the contests, 22 students. Students who competed only in Pytagoriade were twice as many who just competed in t
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