1. Someone writes the word "mathematics" in a row without spaces. Like this:

MATHEMATICS MATHEMATICS MATHEMATICS...

What will be the $2023^{rd}$ letter in this chain?
Solution. Obviously, the word «mathematics» contains 10 letters. Thus, the number divisible by 10 without a remainder and closest to the number 2023 is the number 2020. After that, we need to count 3 more digits from the beginning of the word - 2023-2020=3. From this, it is clear that the required letter will be the letter T.

Answer: the letter T.