Announcements
Regional Olympiad
1. a) Imagine the number 2025 as the sum of several (more than one) consecutive natural numbers (at least 3 examples) [3]
b) Find out if there is a way to make this sum so that it contains more than 63 terms. [2]
2. A 4x4 square is divided into 16 cells. Color these cells black and white so that each black cell has three white neighbors, and each white cell has exactly one black neighbor. (Adjacent cells are considered to have a common side.) [3]
3. There are 70 children in the summer camp. Of these, 27 are involved in drama clubs, 32 sing in the choir, 22 are fond of sports. There are 10 children from the choir in the drama club, 6 athletes in the choir, 8 athletes in the drama club; 3 athletes attend both the drama club and the choir. How many kids don't sing in the choir, don't get involved in sports, and don't play in a drama club? [4]
4. Masha wrote 10 numbers on the blackboard. Pasha noticed that the sum of any nine numbers is odd. Is the sum of all written numbers even or odd? [4]
5. If you open the faucet with cold water, the tub will fill in 10 minutes, and if you open the faucet with hot water, it will fill in 15 minutes. If you remove the plug, the bath is completely drained in 12 minutes. How long will it take to fill the tub if you open both taps and pull out the plug?[4]