[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
[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 379: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): failed to open stream: No such file or directory
[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(70748da9cacc39e6e2a55b2dbc5a249e.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/70748da9cacc39e6e2a55b2dbc5a249e.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): failed to open stream: No such file or directory
[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(4b4ceaa0a87c4f90807f093c231c02c5.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): failed to open stream: No such file or directory
[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(4b4ceaa0a87c4f90807f093c231c02c5.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): failed to open stream: No such file or directory
[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(4b4ceaa0a87c4f90807f093c231c02c5.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): failed to open stream: No such file or directory
[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(4b4ceaa0a87c4f90807f093c231c02c5.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): failed to open stream: No such file or directory
[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(4b4ceaa0a87c4f90807f093c231c02c5.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): failed to open stream: No such file or directory
[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(4b4ceaa0a87c4f90807f093c231c02c5.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 232: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 235: fopen([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): failed to open stream: No such file or directory
[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(4b4ceaa0a87c4f90807f093c231c02c5.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
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 295: chdir(): No such file or directory (errno 2)
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 297: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.tex): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 298: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.aux): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 299: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.log): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 300: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.dvi): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 301: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.ps): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/latexrender/class.latexrender.php on line 302: unlink([ROOT]/latexrender//tmp/4b4ceaa0a87c4f90807f093c231c02c5.png): No such file or directory
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4688: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3823)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4690: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3823)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4691: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3823)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 4692: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3823)
forum.virtualchallengemeets.com • View topic - AIME II 2010 #8

AIME II 2010 #8

American Mathematics Contest & American Invitational Mathematics Examination. See for more information
Note:USAMO/IMO-level questions need to go in the Olympiad section.

AIME II 2010 #8

Postby stupidityismygam » Wed May 05, 2010 2:50 am

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].
my avatar is pretty awesome
tytia
User avatar
stupidityismygam
Ubiquitous Spammer
 
Posts: 1413
Joined: Tue Nov 21, 2006 8:02 pm

Re: AIME II 2010 #8

Postby stupidityismygam » Wed May 05, 2010 1:00 pm

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]
my avatar is pretty awesome
tytia
User avatar
stupidityismygam
Ubiquitous Spammer
 
Posts: 1413
Joined: Tue Nov 21, 2006 8:02 pm


Return to AMC/AIME

Who is online

Users browsing this forum: No registered users and 4 guests

cron