document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133157>Question 1133157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 10 steps from ground level to the top. The 6th step is under repair and only can be crossed but not step on. <BR>\n" );
document.write( "Mike walks up the steps with one or two steps at a time. How many different ways can he walk up to the top? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750339 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=750339\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "In the classic problem like this, none of the steps is under repair.<br><BR>\n" );
document.write( "If Mike can walk up the steps either one or two steps at a time, then he can get to step n from either step (n-1) or  step (n-2).  Using that reasoning....<br><BR>\n" );
document.write( "He can only get to step 1 from \"step 0\": 1 way<br><BR>\n" );
document.write( "He can get to step 2 from either step 0 or step 1: 1+1 = 2 ways<br><BR>\n" );
document.write( "He can get to step 3 from either step 1 or step 2: 1+2 = 3 ways<br><BR>\n" );
document.write( "He can get to step 4 from either step 2 or step 3: 2+3 = 5 ways<br><BR>\n" );
document.write( "... and so on.  The pattern you get is the Fibonacci sequence.<br><BR>\n" );
document.write( "You can solve your problem using the same logic; but now you can't land on the 6th step.  That will change the numbers in two ways:<br><BR>\n" );
document.write( "(1) You can only get to the 7th step from the 5th step; and<BR>\n" );
document.write( "(2) You can only get to the 8th step from the 7th step.<br><BR>\n" );
document.write( "If you understand the process, it should be easy to determine the total number of ways he can reach the top. </SPAN>\n" );
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