document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206283>Question 1206283</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, not sure how to tackle the working out for this question: I take a tablet every 10 days. If I take my first tablet on Monday and have 25 tablets, on what day will I take the last tablet. The answer my teacher gave is a Wednesday. Should I use modular arithmetic to solve, very stuck. Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843607 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52794)</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=843607\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Hi, not sure how to tackle the working out for this question: <BR>\n" );
document.write( "I take a tablet every 10 days. If I take my first tablet on Monday and have 25 tablets, <BR>\n" );
document.write( "on what day will I take the last tablet. <BR>\n" );
document.write( "The answer my teacher gave is a Wednesday. Should I use modular arithmetic to solve, very stuck. Thank you.<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;O-o-p-s !\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I agree with the @greenestamps notice, saying that the period in this problem is 10 days, not 9.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;@greenestamps, thanks for noticing my fault.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Having it, I re-wrote my solution, so now you see the updated version.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "    |  To start solving, notice that taking a tablet every 10 days means            |\r\n" );
document.write( "    |  that the process of taking tablets is periodical with the period of 10 days. |\r\n" );
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document.write( "Imagine that the days are coded in this natural way, using numbers from 1 to 7 \r\n" );
document.write( "instead of the days standard naming\r\n" );
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document.write( "    Mo Tu We Th Fr Sa Su     (*)\r\n" );
document.write( "     1  2  3  4  5  6  7\r\n" );
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document.write( "Next, imasgine that you have long sequence of these numbers, repeating in this natural order\r\n" );
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document.write( "     1  2  3  4  5  6  7  1  2  3  4  5  6  7  1  2 . . . . \r\n" );
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document.write( "Then your day in this sequence is this coding number  (10*24+1 mod 7)\r\n" );
document.write( "(i.e. 24 intervals of 10 days plus the next day, and the sum is taken modulo 7).\r\n" );
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document.write( "Multiply 10*24 and add 1.  You will get 241.\r\n" );
document.write( "Find the remainder after division 241 by 7. \r\n" );
document.write( "The division is 241 = 34*7 + 3.\r\n" );
document.write( "Thus the remainder is 3.\r\n" );
document.write( "In other words, (10*24+1 mod 7) = 3.\r\n" );
document.write( "The remainder \"3\" is the code for the 3-rd day in the sequence (*).\r\n" );
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document.write( "Hence, you will take your last tablet on Wednesday.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "Nice problem.\r<BR>\n" );
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document.write( "Yes, &nbsp;the idea is correct to use modular arithmetic.\r<BR>\n" );
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document.write( "But still there is an underwater stone &nbsp;(a trap) &nbsp;which should be treated accurately.\r<BR>\n" );
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document.write( "The stone is to determine &nbsp;CORRECTLY &nbsp;that the day of interest is &nbsp;24*10+1 &nbsp;(not &nbsp;25*10).\r<BR>\n" );
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document.write( "After that, &nbsp;applying modular arithmetic will lead you to the answer quickly and straightforward.\r<BR>\n" );
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