Shapovalovo $A . B$. The numbers from 1 to 37 were written in a row such that the sum of any initial segment of numbers is divisible by the next number in the sequence.

What number is in the third position if the first position is occupied by the number 37, and the second by 1? #
Let the last place in the line be occupied by the number $x$. The sum of all numbers in the line, except for $x$, is divisible by $x$; therefore, the sum of all numbers in the line, which is

$1+2+\ldots+37=37 \cdot 19$, is also divisible by $x$. Hence, $x=19$, since 37 is already placed in the first position. The third position is occupied by a divisor of the number

$37+1=38=19 \cdot 2$, different from 1 and 19, which are in other positions.

## Answer

2.