"Let A_0=(0,0). Distinct points A_1,A_2,\dots lie on the x-axis, and distinct points B_1,B_2,\dots lie on the graph of y=\sqrt{x}. For every positive integer n,\ A_{n-1}B_nA_n is an equilateral triangle. What is the least n for which the length A_0A_n\geq100?"

Taken from AoPS.

Question

"Let A_0=(0,0). Distinct points A_1,A_2,\dots lie on the x-axis, and distinct points B_1,B_2,\dots lie on the graph of y=\sqrt{x}. For every positive integer n,\ A_{n-1}B_nA_n is an equilateral triangle. What is the least n for which the length A_0A_n\geq100?"

Taken from AoPS.

anonymous · Answer

Woops, haha, give me some time to format. Don't know how to use LaTeX :c.

anonymous · Answer

attachment

dumbcow · Answer

can we assume the points have integer coordinates?
or can An be some point (1.42,0)

anonymous · Answer

n has to be an integer, yes.

dumbcow · Answer

n = 17

anonymous · Answer

Yes! http://www.artofproblemsolving.com/Wiki/index.php/2008_AMC_12B_Problems/Problem_24