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2003 AMC 10A Question 23

AMC10 · 2003 AMC 10A

Question 23

A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For example, in the figure we have $3$ rows of small congruent equilateral triangles, with $5$ small triangles in the base row. How many toothpicks would be needed to construct a large equilateral triangle if the base row of the triangle consists of $2003$ small equilateral triangles?

Question illustration
  1. $1{,}004{,}004$
  2. $1{,}005{,}006$
  3. $1{,}507{,}509$
  4. $3{,}015{,}018$
  5. $6{,}021{,}018$