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Mar8-12, 04:13 PM
You have probably seen these candy machines before. Tubes
that contain candies of different colors and drop candies into
a receiver once you inserted the coin.
I was watching these more than a quarter of an hour at lunch
time (waiting for someone to buy candy) and thought that I
could come up with a simple algorithm to mimic these candies
Turned out not so.
To simplify things, I started out with just one tube with slots
that can hold one candy at a time. Let say we have a tube of
7 slots and 5 candies filling the top five. Then the candies
are allowed to drop freely. That is each candy can drop 1, 2 or
more slots at a time if there are spaces.
| o | 1
| o | 2
| o | 3
| o | 4
| o | 5
| | 6
| | 7
I figured that the movement of the bottom candy
decides how many step the upper ones can skip/drop.
I calculated that there are 20 possible distributions
and the original one:
12345 <--- starting.
12346 <--- bottom candy drop one slot.
12347 <--- bottom candy drop two slots.
34567 <---- All bottom slots a filled. Stop.
That much I figured out, and there is a clear pattern of the
sequences here, but for the last few hours I couldn't come up
with a general algorithm for a tube with n slots filled and m
My first (cheese eating) surrending act was looking for some
quick answer in stat books. Sure enough, I got the number
of all possible distributions there, but the algorithm has
been giving me the stump since.
I am looking for any excuse not to work this afternoon.
I am sure that once the algorithm is found it will turn
out to be so simple that I should tear off the rest of my
hair in shame.
Any suggestion help would be greatly appreciated.
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