document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53377>Question 53377</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Linae, the Kougra from Shenkuu, went shopping for Kou-jong tiles at the local toy shop the other day. The kou-jong tiles were on sale for only 28 Neopoints each. \r<BR>\n" );
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document.write( "However, she got it in her head that, for good luck, the total amount of Neopoints she must spend must be a number where all of the digits are the same. \r<BR>\n" );
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document.write( "With that in mind, what is the minimum number of tiles she must buy?\r<BR>\n" );
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document.write( "Please help, I cant figure this out!<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 #35666 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=35666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I think this is a really neat problem.  Let x = number of tiles purchased.  Then the total cost of the tiles would be 28x, which must be the same digit repeating.  The total cost will be <BR>\n" );
document.write( "28x = k, or 28x = kk, or 28x = kkk, or 28x = kkkk, etc.\r<BR>\n" );
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document.write( "Therefore, you must find a number, such that <BR>\n" );
document.write( "x = k/28, or kk/28, or kkk/28, or kkkk/28, etc.\r<BR>\n" );
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document.write( "This can also be written as <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+k%2F%284%2A7%29 ALIGN=MIDDLE  ALT=\"x=+k%2F%284%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+kk%2F%284%2A7%29+ ALIGN=MIDDLE  ALT=\"x=+kk%2F%284%2A7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+kkk%2F%284%2A7%29+ ALIGN=MIDDLE  ALT=\"x=+kkk%2F%284%2A7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+kkkk%2F%284%2A7%29+ ALIGN=MIDDLE  ALT=\"x=+kkkk%2F%284%2A7%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > etc.\r<BR>\n" );
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document.write( "The problem then is to find a number with repeating digits that is evenly divisible by 7 and 4.  Moreover, since the number must also be divisible by 4, it means that the value of k must be 4 times the number 1 or 11 or 111 or 1111, where you are looking for the smallest such number that is divisible by 7.  \r<BR>\n" );
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document.write( "So try dividing 11/7, which does not go evenly.\r<BR>\n" );
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document.write( "Try 111/7, which does not go evenly.<BR>\n" );
document.write( "Likewise continue with, 1111/7, 11111/7, 111111/7, etc. until you find a number that is divisible by 7.  The latter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=111111%2F7=+15873 ALIGN=MIDDLE  ALT=\"111111%2F7=+15873\"   DISABLED_style= \"max-width:90%; height:auto;\" > divides evenly.  \r<BR>\n" );
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document.write( "The solution to the problem is 15873 tiles, whose cost is 15873*28 = 444444.\r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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