Problem 540

Variant 9.4.4. An empty $3 \times 57$ table is drawn on the board. Masha wants to fill its cells with numbers, following these rules:

- each of the numbers $1, 2, 3, \ldots, 171$ must be present in the table;
- the number 1 must be in the bottom-left cell of the table;
- for any natural number $a \leqslant 170$, the numbers $a$ and $a+1$ must be in adjacent cells.

(a) (1 point) What is the largest number that can be in the cell adjacent to the number 1?

(b) (3 points) We will call a cell of the table good if the number 171 can be in it. How many good cells are there?