1. Each worker on the construction site has at least one construction specialty. 10 people have the specialty of a mason, 9 - the specialty of a painter, 8 - the specialty of a plasterer. It is known that at least four people have the specialties of a mason and a plasterer simultaneously, at least five people - the specialties of a mason and a painter, and at least three people - the specialties of a painter and a plasterer. What is the maximum number of workers that can be on the construction site under these conditions?
# Answer 18.

Solution: According to the principle of inclusion-exclusion, the total number of workers is K+M+S - KM-KS-MS + KMS = 10+9+8-4-5-3 + KMS = 15 + KMS. Note that the number of workers proficient in all three specialties cannot exceed 3.