document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=163599>Question 163599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ok. i've got a tough one.\r<BR>\n" );
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document.write( "A man selling fruit has only three weights, but with them he can weigh any whole number of kilograms from 1 kg up to 13 kg inclusive on his balance. what weights does he have?\r<BR>\n" );
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document.write( "please HELP!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148565 by </B><A HREF=/tutors/aboutme.mpl?userid=J2R2R><B>J2R2R(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=J2R2R><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=J2R2R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=148565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The easiest way to look at this instinctively is to realise that you don’t just ‘add’ weights to weigh; you can ‘subtract’ weights by placing them on the other side.\r<BR>\n" );
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document.write( "If you could only add weights you could have to use 1, 2, 4, etc. as in binary which can represent any integer using 0s and 1s. 1, 1+0, 1+1, 1+0+0, 1+0+1, 1+1+0, 1+1+1 etc. as we are adding all the time.\r<BR>\n" );
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document.write( "Number, add = 2 degrees of freedom.\r<BR>\n" );
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document.write( "But as you can also subtract (putting weights on the other side), you can use the powers of 3 instead of 2 which gives us 1, 3 and 9 to make 13. Subtracting gives us an extra degree of freedom so we can advance in powers of 3.\r<BR>\n" );
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document.write( "Number, add, subtract = 3 degrees of freedom\r<BR>\n" );
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document.write( "1, 3-1, 3, 3+1, 9-3-1, 9-3, 9-3+1, 9-1, 9, 9+1, 9+3-1, 9+3, 9+3+1\r<BR>\n" );
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document.write( "So, how do we subtract a weight – easy, just put it on the side of the item you are weighing.\r<BR>\n" );
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document.write( "E.g. to weigh something of 6 kg, you would place 9 kg on one side and 3 kg on the side with the object you are trying to weigh. When they balance you know the object you are weighing is 6 kg.\r<BR>\n" );
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document.write( "So the answer is 1 kg, 3 kg and 9 kg. </SPAN>\n" );
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