It depends on the mechanical design, but sometimes the design cuts the Hamiltonion circuit at some point, so all you have is a Gray-code-based Hamiltonian path. The cut, should it exist, might be somewhere along the 86-step path. On Fri, May 31, 2019 at 10:15 AM James Propp <jamespropp@gmail.com> wrote:
Actually, now that I'm getting ready to write this up, I realize that I'm confused.
If we've got a Hamiltonian circuit on the 8-cube coming from a Gray code of length 8, and we have a path of length 170 from 00000000 to 11111111, don't we also have a path of length 256-170=86 from 11111111 back to 00000000? Wouldn't traversing this path in reverse give us a path of length 86 from 00000000 to 11111111? So isn't there a solution for The Brain (aka "The Brain Puzzle") that takes only 86 moves?
Jim Propp
On Wed, May 8, 2019 at 11:50 AM James Propp <jamespropp@gmail.com> wrote:
That's perfect!
I see that in particular the Gray-code-based puzzle "The Brain Puzzler" takes 170 moves to solve:
https://everything2.com/title/The+Brain+Puzzler
Thanks, Michael!
Jim
On Wed, May 8, 2019 at 11:06 AM Michael Kleber <michael.kleber@gmail.com
wrote:
Membership in http://oeis.org/A000975 is definitely the way to go. The description of the sequence makes it clear that it's just saying 170 is 10101010 in binary, but the comments section offers plenty of examples of cool things about those alternating-0s-and-1s numbers.
--Michael
On Wed, May 8, 2019 at 10:41 AM Mike Stay <metaweta@gmail.com> wrote:
On Wed, May 8, 2019 at 8:29 AM James Propp <jamespropp@gmail.com> wrote:
I’ve agreed to host Carnival of Mathematics #170 next month, and I’m wondering whether the number 170 has any especially nice properties
that
might deserve mention.
The number 170 has its own Wikipedia page, but none of the mathematical properties listed there appealed to me.
I might say a little about writing numbers as sums of two squares, but I’d prefer something a little more exciting.
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