Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

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

movement.

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.

12356

12456

13456

23456

12347 <--- bottom candy drop two slots.

12357

12457

13457

23457

12367

12467

13467

23467

12567

13567

23567

14567

24567

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

slots empties.

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.

Michuco

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# Candy Machine Algorithm

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