Art of Problem Solving
Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Mock AIME 1 2006-2007 Problems/Problem 11: Difference between revisions

← Older editNewer edit →
Altheman (talk | contribs)
44 edits
No edit summary
mNo edit summary
Line 1: Line 1:
11. Let <math>\mathcal{S}_{n}</math> be the set of strings with only 0's or 1's with length <math>n</math> such that any 3 adjacent place numbers sum to at least 1. For example, <math>00100</math> works, but <math>10001</math> does not. Find the number of elements in <math>\mathcal{S}_{11}</math>.
==Problem==
Let <math>\mathcal{S}_{n}</math> be the set of strings with only 0's or 1's with length <math>n</math> such that any 3 adjacent place numbers sum to at least 1. For example, <math>00100</math> works, but <math>10001</math> does not. Find the number of elements in <math>\mathcal{S}_{11}</math>.
==Solution==
{{solution}}


[[Mock AIME 1 2006-2007]]
----
 
*[[Mock AIME 1 2006-2007/Problem 10 | Previous Problem]]
 
*[[Mock AIME 1 2006-2007/Problem 12 | Next Problem]]
 
*[[Mock AIME 1 2006-2007]]

Revision as of 18:41, 22 August 2006

Problem

Let $\mathcal{S}_{n}$ be the set of strings with only 0's or 1's with length $n$ such that any 3 adjacent place numbers sum to at least 1. For example, $00100$ works, but $10001$ does not. Find the number of elements in $\mathcal{S}_{11}$.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Retrieved from "https://wiki.aopstest.com/wiki/index.php?title=Mock_AIME_1_2006-2007_Problems/Problem_11&oldid=9783"