Difference between revisions of "2006 AMC 12B Problems/Problem 25"
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== Problem == | == Problem == | ||
| − | {{ | + | A sequence <math>a_1,a_2,\dots</math> of non-negative integers is defined by the rule <math>a_{n+2}=|a_{n+1}-a_n|</math> for <math>n\geq 1</math>. If <math>a_1=999</math>, <math>a_2<999</math> and <math>a_{2006}=1</math>, how many different values of <math>a_2</math> are possible? |
| + | |||
| + | <math> | ||
| + | \mathrm{(A)}\ 165 | ||
| + | \qquad | ||
| + | \mathrm{(B)}\ 324 | ||
| + | \qquad | ||
| + | \mathrm{(C)}\ 495 | ||
| + | \qquad | ||
| + | \mathrm{(D)}\ 499 | ||
| + | \qquad | ||
| + | \mathrm{(E)}\ 660 | ||
| + | </math> | ||
== Solution == | == Solution == | ||
Revision as of 01:10, 4 February 2010
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Problem
A sequence 
of non-negative integers is defined by the rule 
for 
. If 
, 
and 
, how many different values of 
are possible?
Solution
http://www.unl.edu/amc/mathclub/5-0,problems/H-problems/H-pdfs/2006/HB2006-25.pdf
See also
| 2006 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 24 |
Followed by Last Question |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
