The scent from a blooming lily-of-the-valley bush spreads in a radius of 20 m around it. How many blooming lily-of-the-valley bushes need to be planted along a straight 400-meter alley so that every point along it smells of lily-of-the-valley

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Notice that to meet the conditions of the problem, the distance between adjacent lilies of the valley should not exceed $40 \mathrm{M}$.

## Solution

Let's mentally move the leftmost 20 m of the alley to the right end. Then we will have segments of the alley that are 40 m long, and to the right of each segment, a lily of the valley will grow. Thus, the number of lilies of the valley should be the same as the number of 40 m segments that can fit inside the alley. Since 10 such segments can fit, 10 bushes of lilies of the valley need to be planted.