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<DIV><FONT face=Arial size=2>I work at a deli now, but I'm always thinking math,
so here goes.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>The scales at my deli rounds down weights to the
nearest one hundredth of a pound (yeah, it's an odd mix of U.S. and metric, but
I guess it's standard for U.S. delis). So 0.778 pounds of meat or cheese would
weigh out as 77 hundredths of a pound.</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Suppose I am slicing a block of cheese that
happens to yield perfectly uniform slices weighing precisely 0.03871 pounds
each. I start with an empty scale, and add slices one at a time, staying less
than a pound. The successive readings on the scale are:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>0 3 7 11 15 19 23 27 30 34 38 42 46 50 54 58 61 65
69 73 77 81 85 89 92 96<BR></FONT></DIV>
<DIV><FONT face=Arial size=2>The next reading would be 100, which is a pound or
over, so I stop there. Similarly, if the slices weighed 0.04137 pounds each, I
would get the readings</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>0 4 8 12 16 20 24 28 33 37 41 45 49 53 57 62 66 70
74 78 82 86 91 95 99<BR></FONT><FONT face=Arial size=2></DIV></FONT>
<DIV><FONT face=Arial size=2>of if the slices were a very heavy
0.29337 pounds, I would get the readings</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>0 29 58 88</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>My questions are:</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Given slices of perfectly uniform positive weight,
how many different reading sequences are possible? How are they distributed by
number of readings?</DIV>
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<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
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