Problem 616

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stephanbrumme
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Problem 616

Post by stephanbrumme » Sat Dec 16, 2017 4:55 pm

I am still not sure how to understand this sentence:
An integer n>1 is said to be creative if for any integer m>1 Alice can obtain a list that contains m starting from L={n}.
Does it mean:
  • n can be converted to at least one integer m>1 or
  • n can be converted to every integer m>1
Is it okay if m=n ?
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Animus
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Re: Problem 616

Post by Animus » Sat Dec 16, 2017 5:09 pm

It means:
n can be "converted" to every integer m>1.

Good luck

v6ph1
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Re: Problem 616

Post by v6ph1 » Sat Dec 16, 2017 7:16 pm

Do the rules mean for {8} and {9}, the only valid step is to {2,3}.
And from {2,3} to {8} or to {9}
Or are there more steps allowed for the example?
Last edited by v6ph1 on Sat Dec 16, 2017 8:27 pm, edited 2 times in total.
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hk
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Re: Problem 616

Post by hk » Sat Dec 16, 2017 8:18 pm

No, there are no more steps allowed starting with {8}, without creating a set you have had already.
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v6ph1
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Re: Problem 616

Post by v6ph1 » Sat Dec 16, 2017 8:33 pm

Thanks.

On my reading, there is no creative number, which can generate all integers >1.
(I have a non-formal prove for this in my mind)
As 0 gets rejected, this is obviously false.

Can anyone post one of the creative numbers?
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MHealy
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Re: Problem 616

Post by MHealy » Sat Dec 16, 2017 8:54 pm

I also initially believed there were no creative numbers, so I understand your frustration, but I do not believe it would be right to spoil your discovery of why this is false by providing one (nor, I imagine, do the problem creators, as they did not give such in the problem description).

Good luck!
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sjhillier
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Re: Problem 616

Post by sjhillier » Sat Dec 16, 2017 10:51 pm

v6ph1 wrote:
Sat Dec 16, 2017 8:33 pm
On my reading, there is no creative number, which can generate all integers >1.
If it makes you feel better, I took about two days to convince myself that the answer was not 0. (I did have real work to do at the time too, or I might have been a bit quicker.)

v6ph1
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Re: Problem 616

Post by v6ph1 » Sat Dec 16, 2017 10:57 pm

Got it - [ removed by admin ]
-> Completely solved: Thanks for the non-hints.
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traxex
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Re: Problem 616

Post by traxex » Sun Dec 17, 2017 4:13 am

v6ph1 wrote:
Sat Dec 16, 2017 10:57 pm
Got it - and [here's a small hint nobody asked for]!
-> Completely solved: Thanks for the non-hints.
Did you really have to? Nobody other than you has asked for spoilers. People opening this thread expect to see clarifications about what the problem is asking and only that, you gave them an unexpected and unwelcome hint.
Technically, everyone is full of himself.

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beco
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Re: Problem 616

Post by beco » Sun Dec 17, 2017 4:55 am

stephanbrumme wrote:
Sat Dec 16, 2017 4:55 pm
I am still not sure how to understand this sentence:
An integer n>1 is said to be creative if for any integer m>1 Alice can obtain a list that contains m starting from L={n}.
Does it mean:
  • n can be converted to at least one integer m>1 or
  • n can be converted to every integer m>1
Is it okay if m=n ?
I am with the same problem.

Is there a maximum implicit?

I mean: n can be converted to every integer 1<m<n ?

traxex
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Re: Problem 616

Post by traxex » Sun Dec 17, 2017 5:08 am

beco wrote:
Sun Dec 17, 2017 4:55 am
Is there a maximum implicit?

I mean: n can be converted to every integer 1<m<n ?
No, m can be any positive integer greater than one. So there are infinitely many choices for m.
Technically, everyone is full of himself.

LilStalker
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Re: Problem 616

Post by LilStalker » Sun Dec 17, 2017 10:12 am

Does the development team have the information of how many '0' submission this problem got?
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hk
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Re: Problem 616

Post by hk » Sun Dec 17, 2017 11:44 am

No, we don't keep track of the number and the values of wrong solutions.
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zatalian
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Re: Problem 616

Post by zatalian » Sat Jan 06, 2018 10:02 am

Can i ask how many creative numbers there are <= 10.000?

traxex
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Re: Problem 616

Post by traxex » Sat Jan 06, 2018 10:39 am

Asking for partial results or posting them is explicitly discouraged on this forum.
Technically, everyone is full of himself.

JoshEnglish
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Re: Problem 616

Post by JoshEnglish » Sat Jan 13, 2018 12:56 am

I, too, am stuck on the idea that
An integer n>1 is said to be creative if for any integer m>1 Alice can obtain a list that contains m starting from L={n}
implies that a {n} must generate every integer greater than 1.

By my reading, 4 is creative because {4} can become {2, 2} and satisfy the condition that this list contains "any integer m>1".

traxex
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Re: Problem 616

Post by traxex » Sat Jan 13, 2018 1:46 am

According to this Wikipedia article listing mathematical symbols, $\forall$ can be read as "for all", "for any", "for each", or "for every".

To me it was very clear that the meaning of "for any" in this problem is $\forall$, "for all", "for every"; rather than $\exists$, "for some", "there exists".

On the other hand, this answer on StackExchange gives some examples where the meaning of "any" is less clear, and one comment mentions a book on mathematical writing that discourages the use of "any" because of possible ambiguity.
Technically, everyone is full of himself.

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