Task 1. Electronic clocks show the time: hours, minutes, and seconds, for example, 18:00:00. One day, two digits on the clock went out, and only the digits $2,0,2,2$ (in that exact order) remained. Name the latest moment in the day when this could have happened.

[3 points

(М. А. Калинин)]
Answer: 23:50:22.

Solution. The latest time that electronic clocks can display is 23:59:59. If we look at the time as a six-digit number, two moments of time are compared in the same way as ordinary numbers: the time is greater, the greater the first digit; if the first digits are the same, the second is compared, and so on. Therefore, we will try to keep as many of the first digits of $23: 59: 59$ as possible. The maximum number of first digits that can be left is three, since otherwise more than two digits different from 2 and 0 will remain. Let's try to find a time that starts with $23: 5 *: * *$. The digits 3 and 5 must definitely go out, so the remaining ones must be $2,0,2,2$ in exactly this order, i.e., the clock should show: 23:50:22.