A ruler with no mark on it can measure its own length $$AB$$. A ruler with only one mark on it can measure $$3$$ lengths $$AB,AC,BC$$. A ruler with two marks on it can measure $$6$$ lengths $$AB,AC,CD,DB,AD,CB$$. Then the number of lengths a ruler with $$4$$ marks on it can measure is
Correct Answer: 15
Solution
Four internal marks together with the two endpoints give $$6$$ points on the ruler. Every pair of points determines one measurable length. Therefore, the number of lengths is $$\binom{6}{2}=15$$.
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