document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=58446>Question 58446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having trouble with a word problem, not from a book and don't understand how to find an equation for this one:<BR>\n" );
document.write( "Use the digits 0,1,2,3,4,5,6,7,8,9 and form a 10 digit number.  It must be divisible by every number starting at 1 through 18, including 18.  Each digit must be used only one time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40039 by </B><A HREF=/tutors/aboutme.mpl?userid=jenrobrody><B>jenrobrody(19)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jenrobrody><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=40039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is not really an easy equation for this one, however we use a trial-and-error approach:<BR>\n" );
document.write( "The 10 digit number needs to be divisible by numbers 1-18:<BR>\n" );
document.write( "All numbers are divisible by one.<BR>\n" );
document.write( "Even numbers are divisible by two.<BR>\n" );
document.write( "If the sum of all the digits are divisible by 3, then the number is.(If we use the digits 0,1,2,3,4,5,6,7,8,and 9 in any order, their sum is 0+1+2+3+...=45 divisible by three, so any number with those ten digits is divisible by three.)<BR>\n" );
document.write( "If the last two digits of a number is divisible by 4, the number is.<BR>\n" );
document.write( "If the number ends in 5 or 0, the number is divisible by 5.<BR>\n" );
document.write( "If the number is divisible by 2 and 3, then the number is divisible by 6.<BR>\n" );
document.write( "We are going to just have to check divisiblility by 7 the hard way.<BR>\n" );
document.write( "If the last three digits of a number is divisible by 8, the number is.<BR>\n" );
document.write( "If the sum of all the digits are divisible by 9, then the number is. (Again, the digits 0,1,2,3,4,5,6,7,8,and 9 in any order will give a ten digit number that is divisible by 9)<BR>\n" );
document.write( "If the last digit ends in 0(even and divisble by 5), then the number is divisible by 10.<BR>\n" );
document.write( "We are going to just have to check divisiblility by 11,13,and 17 the hard way.<BR>\n" );
document.write( "If the number is divisible by 4 and 3, then the number is divisible by 12.<BR>\n" );
document.write( "If the number is divisible by 7 and 2, then the number is divisible by 14.<BR>\n" );
document.write( "If the number is divisible by 5 and 3, then the number is divisible by 15.<BR>\n" );
document.write( "If the last 4 digits of the number are divisible by 16, then the number is.<BR>\n" );
document.write( "If the number is divisible by 9 and 2, then the number is divisible by 18.\r<BR>\n" );
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document.write( "In summary:<BR>\n" );
document.write( "To be divisible by numbers 1 through 18 a number needs:<BR>\n" );
document.write( "1. to end in zero (divisible by 2,5,and 10)<BR>\n" );
document.write( "2. to be divisible by 16. (divisible by 2,4,8,16)<BR>\n" );
document.write( "3. to use all ten digits 0 through 9. (divisible by 3,9)<BR>\n" );
document.write( "----the first three combine to give a number divisible by 1,2,3,4,5,6,8,9,10,12,15,16,18<BR>\n" );
document.write( "4. to be divisible by 7,11,13,17\r<BR>\n" );
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document.write( "A number divisible by 7,11,13,16,and 17 has all of those factors, so we start with 7x11x13x16x17=272272.<BR>\n" );
document.write( "This number does not have 10 digits, so we count by 272272s:<BR>\n" );
document.write( "544544,816816,....., until we have a ten digit number that ends in 0....<BR>\n" );
document.write( "im trying to find it for you... </SPAN>\n" );
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