Planting Trees Problem Calculator

Find how many trees fit along a path from its length and the spacing between trees. Handles four classic word problem cases: both ends, one end, neither end, and a circular path, with the number of gaps and step by step reasoning.

Input

Enter the total length of the path, the spacing between trees, and the planting pattern to find the number of trees.

Length L

Spacing d

Planting pattern

Use the same unit (such as meters) for length and spacing. When the length is a multiple of the spacing, the trees fit evenly.

Result

Both ends

Number of trees

Number of gaps

Length L

100

Spacing d

How to solve

Dividing the length 100 by the spacing 5 gives 20 gaps.

Planting at both ends, the number of trees is the gap count 20 plus 1, which is 21.

The relationship between gaps and trees depends on the pattern: both ends gives one more, neither end gives one less, while one end and circular give the same count.

How it works

Divide the total length L by the spacing d to get the number of gaps between trees.
When trees are planted at both ends, the number of trees is one more than the number of gaps.
When trees are planted at only one end, the number of trees equals the number of gaps.
When neither end has a tree, the number of trees is one less than the number of gaps.
On a circular path the start and end meet, so the number of trees equals the number of gaps.
If the length is not divisible by the spacing, the trees do not fit evenly and a note is shown.

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