document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=39128>Question 39128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A set of tiles numbered 1 through 100 is modified repeatedly by the folowing operation: remove all tiles numbered with a perfect square, & renumber the remaining tiles consecutively strarting with 1. Howmany times must the operation be performed to reduce thenumber of tiles in the set to one? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #24555 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=24555\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is no method for this except just doing the procedure...<BR>\n" );
document.write( "The perfect squares are<BR>\n" );
document.write( "1, 4, 9, 16, 25, 36, 49, 64, 81, and 100<BR>\n" );
document.write( "Thus the first time ten tiles are removed and 90 remain.<BR>\n" );
document.write( "The second time nine tiles are removed and 81 remain.<BR>\n" );
document.write( "The third time nine tiles are removed and 72 remain.<BR>\n" );
document.write( "The next time eight tiles are removed and 64 remain.<BR>\n" );
document.write( "The next time eight tiles are removed and 56 remain.<BR>\n" );
document.write( "The next time seven tiles are removed and 49 remain.<BR>\n" );
document.write( "The next time seven tiles are removed and 42 remain.<BR>\n" );
document.write( "The next time six tiles are removed and 36 remain.<BR>\n" );
document.write( "The next time six tiles are removed and 30 remain.<BR>\n" );
document.write( "The next time five tiles are removed and 25 remain.<BR>\n" );
document.write( "The next time five tiles are removed and 20 remain.<BR>\n" );
document.write( "The next time four tiles are removed and 16 remain.<BR>\n" );
document.write( "The next time four tiles are removed and 12 remain.<BR>\n" );
document.write( "The next time three tiles are removed and 9 remain.<BR>\n" );
document.write( "The next time three tiles are removed and 6 remain.<BR>\n" );
document.write( "The next time two tiles are removed and 4 remain.<BR>\n" );
document.write( "The next time two tiles are removed and 2 remain.<BR>\n" );
document.write( "The last time we remove one tile and one remains.\r<BR>\n" );
document.write( "\n" );
document.write( "Now count up the times...18 times? </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );