Tasks here: https://1.shkolkovo.online/public-sto... ➡ Connect for FREE to the Click of the Unified State Exam in Mathematics and get charged with knowledge???? https://3.shkolkovo.online/shelchok-e... ????More details about the Click of the Unified State Exam 2024 here: https://3.shkolkovo.online/shelchok-e... Summer vacation as a ???? GIFT? Easy! For those who connect to the Time of the First - the Summer course is a bonus ???? ????USE: https://3.shkolkovo.online/vremya-per... ????OGE: https://3.shkolkovo.online/vremya-per... ????10 classes: https://3.shkolkovo.online/vremya-per... ❗HURRY UP: the price for VP will increase on JULY 10th ???? ???? Spin the roulette and get an additional discount ????????https://3.shkolkovo.online/fortune?ut... ????Find out more about how to save money here ⬇ https://3.shkolkovo.online/vozvrat-nd... All our current promotions and discounts ???????? https://3.shkolkovo.online/special?ut... ????Feedback from our students???????? https://2.shkolkovo.online/reviews?ut... Telegram channel on mathematics with MO???????? https://t.me/MO_EGE ???? Subscribe to notifications and mailing of useful materials VK???????? https://vk.com/app5898182_-185634090#... Our channels: ✔️Olympiad mathematics with DA: https://shkolkovo.info/yt1 ✔️ Physics with AB: https://shkolkovo.info/yt2 ✔️ Preparation for the OGE for all subjects: https://shkolkovo.info/yt4 ✔️ Social Science with MV: https://shkolkovo.info/yt5 ✔️ Biology with EB: https://shkolkovo.info/yt6 ✔️ Biology and Chemistry Mutagen: https://shkolkovo.info/yt7 ✔️ Easy-USE Mathematics with Ali: https://shkolkovo.info/yt9 ✔️ Mathematics with MO and Russian language with TA (Shkolkovo Main Channel): https://shkolkovo.info/yt10 ✔️ Maxim Koval. Vlog of a math teacher: https://shkolkovo.info/yt11 ✔️ Economics. Shkolkovo Olympiads: https://shkolkovo.info/yt12 ✔️Physics OGE with GK: https://shkolkovo.info/yt13 ✔️History with AB: https://shkolkovo.info/pf ✔️English with SS: https://shkolkovo.info/pg ✔️Computer Science BU: https://shkolkovo.info/tn ✔️Social Science OGE: https://shkolkovo.info/xj 0:00 Hello everyone! 5:10 Problem 10. An invariant that many did not solve at the real USE-2022. We analyze how the difference between two piles changes 10:18 Problem 10. We come up with an example and kill point a), without even using the invariant! 14:28 Problem 10. We use our invariant, which we discussed before point a), to solve point b) 18:15 Problem 10. We analyze how many stones can be in boxes 1, 2, and 3, we get an estimate of the maximum number in box 4. It remains to give an example of how to get 363 stones in pile 4! 28:50 Problem 11. We show in general terms what we get as a result of the operation - this will help us in the following points. We use this notation to come up with an example for point a) 34:45 Problem 11. We use divisibility by 3 to analyze points b) and c) 40:28 Problem 11. We count the number of different results in each of the blocks of 100 in point c). Don't forget to check for matches between blocks 54:05 Problem 12. Discuss how to correctly come up with an example in point a) 56:18 Typo: 101 should be instead of 100. But in this case, the example still doesn't work. Select the sequence members and get an example 59:42 Problem 12. Point b): write the condition in general form and analyze the denominators. Try to find the minimum fraction with a denominator of 8 1:10:18 Problem 12. Point c): get the maximum sum and prove that for absolutely any other numbers the sum will be less 1:21:05 Problem 16. A problem about sequences with a beautiful idea. Transform the condition into arithmetic means and get a condition on the differences between adjacent numbers. Find that the sequence of differences between numbers is decreasing! 1:39:59 Problem 16. Write the maximum sum and get an estimate for r1. 1:49:40 Break for OBED with Gennady 1:58:40 Problem 15. Let's recall the OTA, make an estimate for S, and we have item a) in our pocket 2:01:48 Problem 15. Let's recall the equiremainder sign when dividing by 3 and work only with the remainders A and S 2:05:40 Problem 15. Let's go through the possible options for A and S for each number greater than 1503. Let's make an estimate for A and S 2:20:31 Problem 29. Not a problem, but a ROCKET from the 2015 Unified State Exam. Let's analyze the condition 2:22:17 Problem 29. Let's write down all the numbers and create a system of equations using the condition on their sum. We solve the system and make an example for point a) 2:31:20 Problem 29. Similarly with point a), we write down the systems of equations, and then we estimate the sum of the resulting numbers 2:35:50 Problem 29. We use the same idea from point a). We estimate A and B and finish point c) with an example!