1. The numbers from 1 to 2150 are written on a board. Every minute, each number undergoes the following operation: if the number is divisible by 100, it is divided by 100; if it is not divisible by 100, 1 is subtracted from it. Find the largest number on the board after 87 minutes.
Answer: 2012. Solution. All numbers, the last two digits of which are 86 or less, will transform into numbers ending in 00 within 87 minutes, and in the next step, they will decrease by a factor of 100. In the end, all such numbers will be no more than $2100 / 100=21$ after 87 minutes. Those numbers that end in 87 or more will decrease by 87 over 87 minutes. The largest of such numbers is 2099, and it will turn into 2012 after 87 minutes.