Ponder This

December 2001

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Ponder This Challenge:

Consider chess board of dimension 4 by N.

In a "closed knight's tour", we start at some square of the board, proceed by valid knight's moves, visit each square exactly once, and return to our starting point as the 4N+1st square.

An "open knight's tour" is similar, except that we stop at the 4Nth square, having visited all squares exactly once, and with no requirement that we ever return to the starting square.

Part 1:
For what N is there a closed knight's tour of the 4xN chessboard?

Part 2:
For what N is there an open knight's tour of the 4xN chessboard?

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Challenge: 12/03/2001 @ 3:00 PM EST
Solution: 01/02/2002 @ 9:30 AM EST
List Updated: 1/2/2002 @ 10:15 AM EST

People who answered correctly:

Part 1 Correct
Henry Bottomley (12.3.2001 @ 6:00 PM EDT)
John G. Fletcher (12.4.2001 @ 11:41 PM EDT)
Faron Moller (12.7.2001 @ 3:57 AM EDT)
George Ross (12.7.2001 @ 12:41 PM EDT)
Guarav Agrawal (12.10.2001 @ 1:00 AM EDT)
Jacques Willekens (12.11.2001 @ 8:43 AM EDT)
Dave Biggar (12.11.2001 @ 9:01 AM EDT)
Christopher Howe (12.11.2001 @ 1:38 PM EDT)
Liuwei (12.11.2001 @ 6:00 PM EDT)
Jean Flies (12.13.2001 @ 1:48 PM EDT)
Ionel Santa (12.14.2001 @ 4:27 PM EDT)
Surendar Reddy Nanchary (12.15.2001 @ 6:54 PM EDT)
Greg Matusovsky (12.16.2001 @ 12:02 AM EDT)
Nagendra (12.17.2001 @ 5:51 AM EDT)
Bill Roscoe (12.17.2001 @ 6:36 AM EDT)
Vince Lynch (12.20.2001 @ 11:38 AM EDT)
David Zimmermann (12.21.2001 @ 4:59 PM EDT)
Victor Chang (12.24.2001 @ 6:36 PM EDT)
Oscar Portela Arjona (12.26.2001 @ 5:02 PM EDT)
Arun Sivaramakrishnan (12.28.2001 @ 6:16 AM EDT)
Alexey Vorobyov (12.30.2001 @ 3:42 AM EDT)

Part 2 Correct
Henry Bottomley (12.3.2001 @ 6:00 PM EDT)
Alexis G. Megas (12.4.2001 @ 8:35 AM EDT)
Vladimir Sedach (12.4.2001 @ 11:40 AM EDT)
John G. Fletcher (12.4.2001 @ 11:41 PM EDT)
Vince Lynch (12.5.2001 @ 6:58 PM EDT)
Shmuel Spiegal (12.6.2001 @ 12:53 PM EDT)
Guarav Agrawal (12.7.2001 @ 10:27 AM EDT)
Brian Peltzer (12.10.2001 @ 8:07 AM EDT)
Jacques Willekens (12.11.2001 @ 8:43 AM EDT)
Dave Biggar (12.11.2001 @ 9:01 AM EDT)
Christopher Howe (12.11.2001 @ 1:38 PM EDT)
Liuwei (12.11.2001 @ 6:00 PM EDT)
Samantha Levin (12.13.2001 @ 11:43 AM EDT)
Jean Flies (12.13.2001 @ 1:48 PM EDT)
Ionel Santa (12.14.2001 @ 4:27 PM EDT)
Surendar Reddy Nanchary (12.15.2001 @ 6:54 PM EDT)
Greg Matusovsky (12.16.2001 @ 12:02 AM EDT)
Bill Roscoe (12.17.2001 @ 6:36 AM EDT)
David Zimmermann (12.19.2001 @ 3:26 PM EDT)
Victor Chang (12.24.2001 @ 6:36 PM EDT)
Oscar Portela Arjona (12.26.2001 @ 5:02 PM EDT)
Arun Sivaramakrishnan (12.28.2001 @ 6:16 AM EDT)
Alexey Vorobyov (12.30.2001 @ 3:42 AM EDT)
Alan O'Donnell (12.31.2001 @ 8:14 AM EDT)

Part 2 - Partial Solution
Brad Grimm (12.10.2001 @ 11:20 PM EDT)
Padraic Moran (12.12.2001 @ 10:42 AM EDT)
Daniel Chalk (12.19.2001 @ 5:27 PM EDT)
Prithu (12.27.2001 @ 7:09 AM EDT)
Prakash Jalan (12.28.2001 @ 11:44 AM EDT)
Venkata Subramani Janardhanan (12.30.2001 @ 9:43 AM EDT)
Ajay Gupta (12.31.2001 @ 2:20 AM EDT)
Reejis Stephen (12.31.2001 @ 6:36 AM EDT)

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