document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=83332>Question 83332</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to find the combination to a cylindrical lock with digits from 0-9 printed on each of the cylinders.  Use these clues to open the lock:  \r<BR>\n" );
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document.write( "-the lock has three cylinders<BR>\n" );
document.write( "-the product of the tens digit and the ones digit is 8<BR>\n" );
document.write( "-the three digit number is greater than 256<BR>\n" );
document.write( "-the tens digit is the sum of the hundreds digit and the ones digit\r<BR>\n" );
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document.write( "What is the three-digit combination?\r<BR>\n" );
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document.write( "Thank you for your help...I'm desperate! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #59851 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=59851\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can deduce this in a few steps.<BR>\n" );
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document.write( "Call the three digits H for hundreds, T for tens, and U for units or ones.<BR>\n" );
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document.write( "The first clue (#1) is that you are told that T times U equals 8. That means that T and U are<BR>\n" );
document.write( "factors of 8.  This leads to four possible combinations:<BR>\n" );
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document.write( "T = 1 and U = 8<BR>\n" );
document.write( "T = 2 and U = 4<BR>\n" );
document.write( "T = 4 and U = 2<BR>\n" );
document.write( "T = 8 and U = 1<BR>\n" );
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document.write( "Second (#2) you are told that HTU is greater than 256.  This tells you that H must be at least 2.<BR>\n" );
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document.write( "Third (#3) you are told that T = H + U. Since you know from #2 that H is 2 or greater,<BR>\n" );
document.write( "and from #1 that U is at least 1, then you know that H + U must be at least 3.  Therefore,<BR>\n" );
document.write( "you can say that T must be at least 3.  Return to #1. From the four possible combinations,<BR>\n" );
document.write( "T could be 1 or 2.  But you just eliminated that possibility using #3.  So now    you know<BR>\n" );
document.write( "that the possible combinations of T and U have been reduced to:<BR>\n" );
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document.write( "T = 4 and U = 2<BR>\n" );
document.write( "T = 8 and U = 1<BR>\n" );
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document.write( "So the possible combinations of T and U are 42 and 81.<BR>\n" );
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document.write( "Return to #3 which told you that T = H + U and solve for H by subtracting U from both sides<BR>\n" );
document.write( "to get T - U = H.  You know that T - U must be either 4 - 2 or 8 - 1.  If it is 4 minus 2<BR>\n" );
document.write( "Then H = 4 - 2 which makes H = 2.  In this case HTU becomes 242. But #2 said that HTU<BR>\n" );
document.write( "must be greater that 256.  This leads to the conclusion that the only possible combination<BR>\n" );
document.write( "for T and U that remains in the running is 81.  And since H = T - U, then H = 8 - 1 = 7.<BR>\n" );
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document.write( "You're there! H = 7, T = 8, and U = 1 for the combination 781.<BR>\n" );
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document.write( "Check ...<BR>\n" );
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document.write( "#1 Does T*U = 8?  Yes 8*1 does equal 8.<BR>\n" );
document.write( "#2 Is HTU greater than 256? Yes, 781 is greater than 256.<BR>\n" );
document.write( "#3 Does T = H + U?  Yes 8 does equal 7 + 1.<BR>\n" );
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document.write( "The answer of 781 meets all the criteria that were given in the problem and is a correct<BR>\n" );
document.write( "solution.  Hope this helps you to see your way through the problem.  Cheers! </SPAN>\n" );
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