/sci/ - Science & Math

[Anonymous No.5947313]

A little problem that you guys might be interested!

[Anonymous No.5947320]

>>5947313
I cheated and used python to figure out the solution, and then processsed backward to infer a property and hence, a proof.

Should I give "clues", or let people think to it ? Fun problem, though. Where did you find it ? And what were the "conditions" ?

(I'm not absolutely sure of my proof now, I must rewrite it properly but I'm confident)

[Talimar No.5947325]

Do the cycles require n1 and n2 for completion, or can you simply use either n1 or n2 to create an empty bucket?

Question 2: What number provides a bucket A with more then 2 tokens?

[Anonymous No.5947328]

>>5947325
I don't understand your first question... '~'

Question 2 : 3 for instance. (games ends with 3 coins in bucket 3)
...I think I missed your point too....

[Anonymous No.5947355]

>>5947320
Hmm can you show the code?

[Anonymous No.5947372]

>>5947355
Not any more...
That's why I did it in python, because it's interpreted...
so I just typed the thing as it comes to my mind...

I was creepy as fuck, but correct. But why ? I can write a proper one in C if you want...

[Anonymous No.5947384]

>>5947372
I dont know C :/
But I would appreciate if you show me the print and explain!

[Anonymous No.5947477]

>>5947372
how did you determine if it was going to terminate for a given number of buckets.

[Anonymous No.5947505]

>>5947477

problem states that N is less than 1000

so that would be 999 buckets

[Anonymous No.5947513]

>>5947384
here is a draft (without includes , namespace and shit).
Sorry it's in french (so I deleted the comments)
(adapted from a similar problem, I didn't know deque, very useful)


http://sebsauvage.net/paste/?d803be9e24b4d202#y9pepARwJ1Ba+F/+7TUq81mB/4zdqIQCvb+DelfG9yM=

>>5947477
see the code
I had no idea at first (python), I just told to myself, if it takes too much time, that's bad.

[Anonymous No.5947514]

>>5947513
FYO, it gives me 20 as a result.

The interesting thing is the math proof, though.

[Anonymous No.5947566]

>>5947514
>FYO
Don't ask me, I don't know what it means

[Anonymous No.5947580]

>>947513
I wrote my own script without looking at yours. For n < 1000 I found that the following n lead to all tokens in the same bucket:
1
2
3
4
5
6
9
10
17
18
33
34
65
66
129
130
257
258
513
514

Did you find the same?

[Anonymous No.5947620]

>>5947580
me again

There is definitely some interesting algebra here. I modified my script to count the length of the repeating cycles for n that fail to terminate, then graphed it.

pic related, muh slopes

[Anonymous No.5947624]

>>5947580
yep.
>>5947580
Don't u see the pattern ?

Now, the proof...

[Anonymous No.5947632]

>>5947624
You mean that solutions come in adjacent pairs and the higher value is 2n - 2?

[Anonymous No.5947641]

>>5947632
yeah :
2^k+1,2^k+2
k from 0 to 9
--> 20 solutions

(2^10+1>1000, so end of the story)

why ?...

[Anonymous No.5947682]

anybody still here?

[Anonymous No.5947692]

>>5947682
Not really, but /sci/ is a slow board... you can post, thread'll still be there tomorrow

[Anonymous No.5947720]

>>5947641
it seems like it is because after the first pass around the circle you will have floor((n-1)/2) buckets remaining. which for these values will be a power of two.

From there it looks like it will keep reducing by factors of 2, once it gets to two it's obvious it will terminate.

the rest will eventually hit an odd number and go forever.

[Anonymous No.5947724]

>>5947682
I just saw this thread for the first time (haven't been on today).
I am bad at programming but from what I've read in this thread, it should be a fun exercise to practice my programming and see what I find.

[Anonymous No.5947735]

>>5947720
The idea I used is the same.

>the rest will eventually hit an odd number and go forever.
Maybe I did it in the bad way, but the "forever" part was hard to formalize.
I think there is a more straightforward path that the one I took.

Wait & See for OP...