30 "IDC" kompaniyasida to'rtta ish boshqaruvchi bor. Ulardan Abbos bu kompaniyaga kelganiga 35 yil, A'zam kelganiga 13 yil, Ozod kelganiga 9 yil va Jasur kelganiga bo'lgan. Kompaniyadagi ixtiyoriy o'zgarish ovoz berish yo'li bilan aniqlanadi. Har bir ish boshqaruvchi kompaniyaga kelganiga necha yil bo'lgan bo'lsa, uning shuncha ballga ega bo'ladi. Hozirda barcha o'zgarishlar Abbos ovoz bergan yo' bo'yicha bajariladi. Eng kamida necha yildan keyin Abbos ovoz bergan yo'nalish berish jarayonida g'olib bo'lmasligi mumkin?

Let's analyze the problem step by step: 1. Determine the voting power of each manager: * Abbos: 35 points * A'zam: 13 points * Ozod: 9 points * Jasur: Since Jasur is the newest member of the company, his time in the company must be less than Ozod's, which is 9 years. To find the minimum number of years after which Abbas's vote will not be decisive, let's denote Jasur's time in the company as *x* years, where *x* < 9. The total voting power of the other three managers is: 13 + 9 + x = 22 + x 2. To make Abbas's vote not decisive, his points must be less than or equal to the sum of the other managers' points:$$35 \le 22 + x$$$$x \ge 35 - 22$$$$x \ge 13$$ This is not possible since x < 9. Let denote $$y$$ as the number of years passed until the next time of voting. After $$y$$ years the points for each manager is: * Abbos: $$35 + y$$ points * A'zam: $$13 + y$$ points * Ozod: $$9 + y$$ points * Jasur: $$x + y$$ points For Abbas's vote not to be decisive, we require:$$35 + y \le (13 + y) + (9 + y) + (x + y)$$$$35 + y \le 22 + 2y + x + y$$$$35 + y \le 22 + x + 3y$$$$13 \le 2y + x$$Since $$x < 9$$, in the best case $$x$$ is equal to 0. $$13 \le 2y + 0$$$$13 \le 2y$$$$y \ge 6.5$$We must search for the minimum integer value, which is $$y = 7$$. Therefore, after a minimum of 7 years, Abbas's vote will no longer be decisive. Answer: 7