Problem 6 · 2001 AMC 8
Medium
Arithmetic & Operations
off-by-one
Six trees are equally spaced along one side of a straight road. The distance from the first tree to the fourth is 60 feet. What is the distance in feet between the first and last trees?
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Answer: B — 100 feet.
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Hint 1 of 2
Distance lives in the spaces between trees, not the trees — so don't divide 60 by 4.
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Hint 2 of 2
This is the fencepost idea: between n trees there are n − 1 gaps. First-to-fourth = 3 gaps; first-to-last = 5 gaps.
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Approach: count gaps, not trees
- The 60 feet is split among the gaps between tree 1 and tree 4 — and there are 3 gaps, not 4 (the fencepost rule). So each gap = 60 ÷ 3 = 20 feet.
- First to last (tree 1 to tree 6) spans 5 gaps: 5 × 20 = 100 feet.
- The fencepost principle (n posts → n − 1 gaps) returns everywhere: floors between landings, fence rails, ringing-clock chimes. Always count the spaces.
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