Задание 1.найдите максимальное натуральное число n...

Solving math problems

I need to solve two math problems in Russian. The first task is to find the maximum number n > 100 such that when its last two digits are removed, the number decreases by exactly a factor of 112. The relationship is n = 100*m + r, where m is the number after removing the digits. I'll carefully calculate each step to avoid mistakes.

Finalizing the math solution

I’ve broken it down—n = 112m and r = 12m. For this to work, r must be less than 100, which restricts m to values 1 through 8. The last two digits of 112m must match r, and indeed, they do when m is between 1 and 8. Everything checks out!

Confirming the solution

To ensure n > 100 and maximize it, I choose m = 8, making n = 896. When I remove the last two digits from 896, I get 8, and 896 ÷ 8 = 112. This works. For m ≥ 9, r exceeds 99, so m must stay ≤ 8. It holds valid for n = 896.

Reviewing the conditions

I’ve confirmed that for the operation "stiranii dvukh poslednikh tsifr," m must always be ≤ 8 to avoid r exceeding 99. For m = 1 through 8, multiplying by 112 gives n values ranging from 112 to 896, with 896 being the maximum valid solution. For larger values of m, r would exceed 99.

Thought for 31s