[ $\underline{\text { Counting in two ways }}$ ]

A carpet covers a staircase with 9 steps. The length and height of the staircase are 2 meters. Will this carpet be enough to cover a staircase with 10 steps, with a length and height of 2 meters?
The length of the horizontal sections of the path is 2 meters, and the length of the vertical sections of the path is also 2 meters.

## Solution

Let the path cover a staircase with a certain number of steps, where the length and height of the staircase are both 2 meters. Mentally project the path onto the horizontal and vertical planes. The total length of the horizontal sections of the path is equal to the length of the staircase, i.e., 2 meters, and the length of the vertical sections of the path is equal to the height of the staircase, i.e., also 2 meters. Thus, to cover this staircase regardless of the number of its steps, the path must have a length of no less than $2+2=4$ meters.

## Answer

it is enough.