MathDB
Bee on a Pseudo-Dodecagon

Source: 2015 AMC 12B # 25

February 26, 2015
algebrapolynomialgeometric seriesabsolute valueAMC

Problem Statement

A bee starts flying from point P0P_0. She flies 1 inch due east to point P1P_1. For j1j \ge 1, once the bee reaches point PjP_j, she turns 3030^{\circ} counterclockwise and then flies j+1j+1 inches straight to point Pj+1P_{j+1}. When the bee reaches P2015P_{2015} she is exactly ab+cda\sqrt{b} + c\sqrt{d} inches away from P0P_0, where aa, bb, cc and dd are positive integers and bb and dd are not divisible by the square of any prime. What is a+b+c+da+b+c+d?
<spanclass=latexbold>(A)</span> 2016<spanclass=latexbold>(B)</span> 2024<spanclass=latexbold>(C)</span> 2032<spanclass=latexbold>(D)</span> 2040<spanclass=latexbold>(E)</span> 2048 <span class='latex-bold'>(A)</span>\ 2016 \qquad<span class='latex-bold'>(B)</span>\ 2024 \qquad<span class='latex-bold'>(C)</span>\ 2032 \qquad<span class='latex-bold'>(D)</span>\ 2040 \qquad<span class='latex-bold'>(E)</span>\ 2048