Problem 622

[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?

[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.

[Oliver1978]

Thanks

[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 ) but the decks in between are still a mistery to me.

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

[mohammad.h915]

Can you tell me the how many digits has answer?

[kenbrooker]

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...

[mohammad.h915]

can help me and say what is the largest number that s(n) = 60

[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.