At least how many passengers must occupy a seat in a metro car so that no more can sit down? (Assumptions: a) The "width" of each passenger is 1/6 of the seat width. b) Seated passengers cannot be forced to change their position.)
Two passengers cannot yet occupy the six-seat bench, because no matter how they sit, each of them can occupy at most 2 seats, and the remaining two seats will definitely accommodate another passenger.

![](https://cdn.mathpix.com/cropped/2024_05_02_1fc51a85693eabf5347ag-1.jpg?height=206&width=507&top_left_y=274&top_left_x=798)

However, three passengers are sufficient to occupy the entire bench. Arrange the passengers so that the width of the spaces between them and at the ends of the bench is 1/8 of the width of the six-seat bench.

Thus, the total width of all the spaces considered is

$$
3 \cdot \frac{1}{6} + 4 \cdot \frac{1}{8} = 1
$$

which is indeed the total width of the bench, and since $\frac{1}{8} < \frac{1}{6}$, more passengers will not fit.