[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
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[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/includes/bbcode.php on line 483: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
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[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
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[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
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[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
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[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 280: copy(fc0f827a65326ace9a5e4d64ef36604c.png): failed to open stream: No such file or directory
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[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 236: fputs() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 237: fclose() expects parameter 1 to be resource, bool given
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 280: copy(fc0f827a65326ace9a5e4d64ef36604c.png): failed to open stream: No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 281: chmod(): No such file or directory
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forum.virtualchallengemeets.com • View topic - AIME II 2010 #8

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AIME II 2010 #8

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AIME II 2010 #8

PostPosted: Wed May 05, 2010 2:50 am
by stupidityismygam
Let [unparseable or potentially dangerous latex formula] be the number of ordered pairs of nonempty sets [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] that have the following properties:

[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
The number of elements of [unparseable or potentially dangerous latex formula] is not an element of [unparseable or potentially dangerous latex formula]
The number of elements of [unparseable or potentially dangerous latex formula] is not an element of [unparseable or potentially dangerous latex formula]

Find [unparseable or potentially dangerous latex formula].

Re: AIME II 2010 #8

PostPosted: Wed May 05, 2010 1:00 pm
by stupidityismygam
Suppose [unparseable or potentially dangerous latex formula].

Then, we have that [unparseable or potentially dangerous latex formula]. For the other 10 elements, we must put them in either [unparseable or potentially dangerous latex formula] or [unparseable or potentially dangerous latex formula], but not both. So, there are [unparseable or potentially dangerous latex formula] choices for the arrangement of the elements.

Noticing that at [unparseable or potentially dangerous latex formula] the conditions are not met gives us that the total number of ordered pairs is
[unparseable or potentially dangerous latex formula]
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