2006 AMC 12B Problems/Problem 25

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Problem

A sequence $a_1,a_2,\dots$ of non-negative integers is defined by the rule $a_{n+2}=|a_{n+1}-a_n|$ for $n\geq 1$ . If $a_1=999$ , $a_2<999$ and $a_{2006}=1$ , how many different values of $a_2$ are possible?

$\mathrm{(A)}\ 165 \qquad \mathrm{(B)}\ 324 \qquad \mathrm{(C)}\ 495 \qquad \mathrm{(D)}\ 499 \qquad \mathrm{(E)}\ 660$

Solution

http://www.unl.edu/amc/mathclub/5-0,problems/H-problems/H-pdfs/2006/HB2006-25.pdf

2006 AMC 12B (Problems • Answer Key • Resources)
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2006 AMC 12B Problems/Problem 25

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