document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204816>Question 1204816</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 11 books are to be stored in a shelf where 4 books can be put vertically, so they are all <BR>\n" );
document.write( "as easily accessible, and 6 books can be piled-up, so the most used ones are on the top.<BR>\n" );
document.write( "(a) In how many ways the books can be put in vertical positions?<BR>\n" );
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document.write( "(b) In how many ways the books can be piled-up?<BR>\n" );
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document.write( "(c) In how many ways the books can be put in both positions?<BR>\n" );
document.write( "Your answer is :  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841326 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52782)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "11 books are to be stored in a shelf where 4 books can be put vertically, so they are all <BR>\n" );
document.write( "as easily accessible, and 6 books can be piled-up, so the most used ones are on the top.<BR>\n" );
document.write( "(a) In how many ways the books can be put in vertical positions?<BR>\n" );
document.write( "Your answer is : \r<BR>\n" );
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document.write( "(b) In how many ways the books can be piled-up?<BR>\n" );
document.write( "Your answer is : \r<BR>\n" );
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document.write( "(c) In how many ways the books can be put in both positions?<BR>\n" );
document.write( "Your answer is : <BR>\n" );
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document.write( "Hello, &nbsp;4 + 6 = 10;  &nbsp;but the post tells us about &nbsp;11 &nbsp;books.\r<BR>\n" );
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document.write( "Where is the &nbsp;11-th book ?  &nbsp;&nbsp;Is it missed ? &nbsp;&nbsp;stolen ? &nbsp;&nbsp;annihilated ? &nbsp;&nbsp;remains outside the shelf ?\r<BR>\n" );
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document.write( "<U>Comment from student</U>: &nbsp;&nbsp;that's exactly why i cannot solve this, i was thinking there is <BR>\n" );
document.write( "something wrong with me but seems like an issue with my prof i guess. thanks!\r<BR>\n" );
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document.write( "<U>My response</U>.  &nbsp;&nbsp;It looks like this problem is &nbsp;SELF-CONTRADICTORY, or, &nbsp;at least, &nbsp;poorly worded.\r<BR>\n" );
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document.write( "Report to your professor, &nbsp;or to the author of the textbook, &nbsp;or to the publishing company \r<BR>\n" );
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document.write( "or to other source as a web-site about this deficiency.\r<BR>\n" );
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document.write( "They will award you for your vigilance.\r<BR>\n" );
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document.write( "By the way, it easily can be that the problem assumes that one book may remain outside.\r<BR>\n" );
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document.write( "But, if so, it should be clear from the problem's formulation.\r<BR>\n" );
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document.write( "It should not be as a reader's guess.\r<BR>\n" );
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document.write( "In other words, in this case problem's wording should be different.\r<BR>\n" );
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document.write( "Always remember that Math problem and puzzle are different things.\r<BR>\n" );
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document.write( "What is allowed in puzzles is not always allowed in Math problems.\r<BR>\n" );
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document.write( "In puzzles, the major goal is to perplex a reader, making the problem's description <BR>\n" );
document.write( "confusing and ambiguous.\r<BR>\n" );
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document.write( "In Math problems, &nbsp;the major goal is to &nbsp;TEACH &nbsp;a reader, &nbsp;making the problem description <BR>\n" );
document.write( "as straight, &nbsp;as clear, &nbsp;as precise and as unambiguous as possible, &nbsp;so that any questions <BR>\n" );
document.write( "“ &nbsp;what is this &nbsp;”  &nbsp;and  &nbsp;“ &nbsp;why is this so &nbsp;”  &nbsp;would not arise at all.\r<BR>\n" );
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document.write( "At this forum, &nbsp;significant part of &nbsp;\" problems \" &nbsp;is written &nbsp;(is created and composed) \r<BR>\n" );
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document.write( "by persons whose mathematical education is from reading puzzles.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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