document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40642>Question 40642</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> a designer, attempting to arrange the charaters of his artwork in the form of a grid with equal number of rows and columns, found that 24 characters were left out.  When he tried to add one more row and column, he found that he was short of 25 characters.  Can you find the number of characters used by the designer?<BR>\n" );
document.write( "isbn 0-321-23383-2, fourth edition </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #26153 by </B><A HREF=/tutors/aboutme.mpl?userid=rajagopalan><B>rajagopalan(174)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rajagopalan><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rajagopalan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=26153\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the original grid size = n<BR>\n" );
document.write( "No of charcters = (n*n)+24<BR>\n" );
document.write( "If one row & one colmn are increased grid size = n+1<BR>\n" );
document.write( "No of Characters  = (n+1)*(n+1)- 25\r<BR>\n" );
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document.write( "equating n^2+24 = ((n+1)^2)-25<BR>\n" );
document.write( "we find<BR>\n" );
document.write( "n^2+24 = n^2+2n+1-25<BR>\n" );
document.write( "24+25 = 2n+1<BR>\n" );
document.write( "49-1 = 2n<BR>\n" );
document.write( "24 = n\r<BR>\n" );
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document.write( "No of characters = n^2+24 = 576+24 = 600<BR>\n" );
document.write( "cheers </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );