Deli problem

[Joshua Zucker]

It seems like http://www.research.att.com/~njas/sequences/A117294 is a
sort-of-related sequence, except that it's asking about multiplication
instead of addition?

I like the idea, though, of counting those additive sequences!

I think there could be a relatively simple algorithm for counting
them: start with first term of 0, then second term is between 1 and 99
(or maybe between 0 and 99?  But there are infinitely many different
sequences that have n 0s followed by approximately n 1s and then
approximately n 2s and so on -- n can be any positive integer -- so I
think if we want to make a sequence out of it, we'd have to exclude
those cases?), and given the second term you have an upper and lower
bound on the actual weight per slice, so that gives you a set of
possibilities for the third term, and so on.  Doesn't seem like too
hard a computer programming problem, anyway.

--Joshua Zuzkcer

On 10/20/06, David Wilson <davidwwilson at comcast.net> wrote:
>
>
> I work at a deli now, but I'm always thinking math, so here goes.
>
> 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.
>
> 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:
>
> 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
>
> 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
>
> 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
>
> of if the slices were a very heavy 0.29337 pounds, I would get the readings
>
> 0 29 58 88
>
> My questions are:
>
> Given slices of perfectly uniform positive weight, how many different
> reading sequences are possible? How are they distributed by number of
> readings?
>
>
>
>
>
>
>