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Problem 622

Posted: Thu Apr 12, 2018 8:54 pm
by Oliver1978
From what I gather from the problem description, the outcome of s(n) is 0 if n is odd, else some value > 0. Is this right?

Re: Problem 622

Posted: Thu Apr 12, 2018 9:01 pm
by hk
From the problem description:
Let $s(n)$ be the minimum number of consecutive riffle shuffles needed to restore a deck of size $n$ to its original configuration, where $n$ is a positive even number.
So if $n$ is odd $s(n)$ is not defined.

Re: Problem 622

Posted: Thu Apr 12, 2018 9:05 pm
by Oliver1978
Thanks :)

Re: Problem 622

Posted: Mon Jan 07, 2019 7:47 am
by Jochen_P
Really interesting little problem (imho 15% is a bit low)
In the mean time I know exactly what the maximum deck size for s(n) = 60 is, or any other amount of shuffles for that matter, (No, you can't shuffle this deck by hand or even forklift :D ) but the decks in between are still a mistery to me.

You really could've asked for s(n)=31 :roll:

Re: Problem 622

Posted: Wed Jun 05, 2019 8:27 am
by mohammad.h915
Can you tell me the how many digits has answer?

Re: Problem 622

Posted: Wed Jun 12, 2019 8:45 pm
by kenbrooker
Jochen_P wrote: Mon Jan 07, 2019 7:47 am In the mean time I know exactly what the maximum deck size for s(n) = 60 is, or any other amount of shuffles
for that matter, ... but the decks in between are still a mistery [sic] to me.
"In between" well said; the minimum deck size is also conspicuous...

Re: Problem 622

Posted: Mon Jul 01, 2019 12:48 pm
by mohammad.h915
can help me and say what is the largest number that s(n) = 60

Re: Problem 622

Posted: Sun Apr 13, 2025 3:07 am
by papadil
I presume a "riffle" shuffle is the same as a "perfect" shuffle (first statement of third paragraph). Pet peeve of mine - calling something x, then later y ...
No one else complained so I also presume I'm nitpicking. :)

PS. Looked it up - and a "perfect riffle" shuffle is what is described in the first paragraph.