[ Mathematical logic (miscellaneous) $]$

Let's get acquainted with three people: Alekhin, Belyaev, and Belkin. One of them is an architect, another is an accountant, and the third is an archaeologist. One lives in Belgorod, another in Bryansk, and the third in Astrakhan. We need to find out who lives where and what each person's profession is.

1) Belkin only visits Belgorod occasionally and very rarely, although all his relatives live in this city permanently.
2) For two of these people, the names of their professions and the cities where they live start with the same letter as their surnames.
3) The wife of the architect is Belkin's younger sister.

#
From 1) and 3), it follows that the architect, who is a relative of Belkin, lives in Belgorod, and from 2) it then follows that the archaeologist lives in the city starting with the letter A, i.e., in Astrakhan, and his surname starts with the letter A, i.e., he is Alekhin. We can conclude that the architect Belyaev lives in Belgorod.

## Answer

Belkin - accountant from Bryansk, Belyaev - architect from Belgorod, Alekhin - archaeologist from Astrakhan.