[math-fun] nice little sliding block head exercise
Neil is tabulating the "hardest" 4x4s according to polyomino size histogram. Some of the short ones are tricky. E.g., a four-piecer: http://gosper.org/4x4-3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Five moves to get the tetromino to the lower right, where a move is of one piece along any path. --rwg
Hans reminds me not to underestimate this audience. http://gosper.org/4x4-0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Three pieces, nine(!) moves. --rwg On Thu, Feb 21, 2013 at 1:51 AM, Bill Gosper <billgosper@gmail.com> wrote:
Neil is tabulating the "hardest" 4x4s according to polyomino size histogram. Some of the short ones are tricky. E.g., a four-piecer: http://gosper.org/4x4-3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Five moves to get the tetromino to the lower right, where a move is of one piece along any path. --rwg
What is the objective? On Thu, Feb 21, 2013 at 8:35 PM, Bill Gosper <billgosper@gmail.com> wrote:
Hans reminds me not to underestimate this audience. http://gosper.org/4x4-0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Three pieces, nine(!) moves. --rwg
On Thu, Feb 21, 2013 at 1:51 AM, Bill Gosper <billgosper@gmail.com> wrote:
Neil is tabulating the "hardest" 4x4s according to polyomino size histogram. Some of the short ones are tricky. E.g., a four-piecer: http://gosper.org/4x4-3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Five moves to get the tetromino to the lower right, where a move is of one piece along any path. --rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Fri, Feb 22, 2013 at 11:12 AM, Allan Wechsler <acwacw@gmail.com> wrote:
What is the objective?
I think that's the essence of the problem: Find a set of 9 consecutive moves that does not repeat the same position twice (where a move is of one piece along any path, and presumably moving to a fractional position isn't allowed). http://gosper.org/4x4-0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0.gif On Thu, Feb 21, 2013 at 8:35 PM, Bill Gosper <billgosper@gmail.com> wrote:
Hans reminds me not to underestimate this audience. http://gosper.org/4x4-0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Three pieces, nine(!) moves. --rwg
On Thu, Feb 21, 2013 at 1:51 AM, Bill Gosper <billgosper@gmail.com> wrote:
Neil is tabulating the "hardest" 4x4s according to polyomino size histogram. Some of the short ones are tricky. E.g., a four-piecer: http://gosper.org/4x4-3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Five moves to get the tetromino to the lower right, where a move is of one piece along any path. --rwg
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
No no, the goal is to get the piece in the top-left down to the bottom-right. See other email from rwg. --Michael On Fri, Feb 22, 2013 at 11:17 AM, Robert Munafo <mrob27@gmail.com> wrote:
On Fri, Feb 22, 2013 at 11:12 AM, Allan Wechsler <acwacw@gmail.com> wrote:
What is the objective?
I think that's the essence of the problem:
Find a set of 9 consecutive moves that does not repeat the same position twice (where a move is of one piece along any path, and presumably moving to a fractional position isn't allowed).
http://gosper.org/4x4-0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0.gif
On Thu, Feb 21, 2013 at 8:35 PM, Bill Gosper <billgosper@gmail.com> wrote:
Hans reminds me not to underestimate this audience. http://gosper.org/4x4-0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Three pieces, nine(!) moves. --rwg
On Thu, Feb 21, 2013 at 1:51 AM, Bill Gosper <billgosper@gmail.com> wrote:
Neil is tabulating the "hardest" 4x4s according to polyomino size histogram. Some of the short ones are tricky. E.g., a four-piecer: http://gosper.org/4x4-3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Five moves to get the tetromino to the lower right, where a move is of one piece along any path. --rwg
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Forewarned is worth an octopus in the bush.
If moving 1 piece pushes/moves N-1 other pieces, does that count as 1 move or N moves?
-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun- bounces@mailman.xmission.com] On Behalf Of Bill Gosper Sent: Thursday, February 21, 2013 1:52 AM To: math-fun@mailman.xmission.com Subject: [math-fun] nice little sliding block head exercise
Neil is tabulating the "hardest" 4x4s according to polyomino size histogram. Some of the short ones are tricky. E.g., a four-piecer: http://gosper.org/4x4-3,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0.gif . Five moves to get the tetromino to the lower right, where a move is of one piece along any path. --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (5)
-
Allan Wechsler -
Bill Gosper -
Huddleston, Scott -
Michael Kleber -
Robert Munafo