[Inclusion-Exclusion Principle] [Arithmetic. Mental calculation, etc.]

In a group of 50 children, some know all the letters except "r", which they simply skip when writing, while others know all the letters except "k", which they also skip. One day, the teacher asked 10 students to write the word "кот" (cat), 18 other students to write the word "рот" (mouth), and the rest to write the word "крот" (mole). It turned out that the words "кот" and "рот" were each written 15 times. How many children wrote their word correctly?
The word "крот" was not written correctly by anyone, because no one can write both the letter "p" and the letter "к" at the same time. The word "рот" or "кот" should have been written by $10+18=28$ people. Note that only

| the words "рот", "кот", and "от" were written. The first two words were written 15 times each, so the word "от" was written by 50 - 15 - 15

$=20$ kids out of 28. Therefore, only 8 kids managed to complete their task.

## Answer

8 kids.