3. Here is a problem from S. A. Rachinsky's problem book (late 19th century): "How many boards 6 arshins long and 6 vershoks wide are needed to cover the floor of a square room with a side of 12 arshins?" The answer to the problem is: 64 boards. Determine from these data how many vershoks are in an arshin.
Solution. The area of the room is $12 \cdot 12=144$ square arshins. Therefore, the area of each board is $144 / 64=2.25$ square arshins. Since the length of the board is 6 arshins, its width should be $2.25 / 6=3 / 8=6 / 16$ arshins. Thus, 6 vershoks make up $6 / 16$ arshins, meaning 1 vershok is $1 / 16$ arshin.

Another solution. Note that the total area of the boards covering the room does not depend on their arrangement. Therefore, we can assume that they lie in two rows, with 32 boards in each row. The length of each row is equal to the side of the room (12 arshins), and at the same time, it is 32 times greater than the width of the board (6 vershoks). Thus, 12 arshins are 32 times greater than 6 vershoks. Therefore, 6 arshins are 16 times greater than 6 vershoks, meaning an arshin is 16 times greater than a vershok.

Answer: there are 16 vershoks in an arshin.