11-1100/Assignment I - Permutation Counting - Revision history

Tholden: Assignment I - Permutation Counting moved to 11-1100/Assignment I - Permutation Counting

2011-10-13T15:39:56Z

Assignment I - Permutation Counting moved to 11-1100/Assignment I - Permutation Counting

← Older revision	Revision as of 11:39, 13 October 2011
(No difference)

2011-10-11T04:03:31Z

← Older revision		Revision as of 00:03, 11 October 2011
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	The puzzle that I have chosen is a 2x2x3 variant of the Rubik's cube. Below is a sketch of how I have labelled.		The puzzle that I have chosen is a 2x2x3 variant of the Rubik's cube. Below is a sketch of how I have labelled it.

	[[2x2x3 Permutation Puzzle]]		[[2x2x3 Permutation Puzzle]]

2011-10-11T04:03:16Z

← Older revision		Revision as of 00:03, 11 October 2011
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	First, the class of permutations is defined, along with how to multiply them and take their inverses. Then, algorithm is spelled out.		First, the class of permutations is defined, along with how to multiply them and take their inverses. Then, algorithm is spelled out.

	The algorithm yields that their are '''39016857600''' different configurations of the 2x2x3 puzzle. The ~~algorithm~~ was subsequently checked with the Rubik's cube generators given on [http://www.math.toronto.edu/~drorbn/Talks/Mathcamp-0907/NCGE.pdf the handout] and the correct numbers were outputted.		The algorithm yields that their are '''39016857600''' different configurations of the 2x2x3 puzzle. The implementation was subsequently checked with the Rubik's cube generators given on [http://www.math.toronto.edu/~drorbn/Talks/Mathcamp-0907/NCGE.pdf the handout] and the correct numbers were outputted.

2011-10-11T04:02:20Z

2011-10-11T03:58:12Z

← Older revision		Revision as of 23:58, 10 October 2011
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	The puzzle that I have chosen is a 2x2x3 variant of the Rubik's cube. Below is a sketch of how I have labelled ~~it along with the permutation generators~~.		The puzzle that I have chosen is a 2x2x3 variant of the Rubik's cube. Below is a sketch of how I have labelled.

	[[2x2x3 Permutation Puzzle]]		[[2x2x3 Permutation Puzzle]]
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	Here are the generators ~~again~~:		Here are the generators:

	g1 = [1,2,3,4,12,22,7,8,6,11,21,28,13,14,15,16,17,18,5,10,20,27,23,24,25,26,9,19,29,30,31,32]		g1 = [1,2,3,4,12,22,7,8,6,11,21,28,13,14,15,16,17,18,5,10,20,27,23,24,25,26,9,19,29,30,31,32]
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	[[NCGE Python Code]]		[[NCGE Python Code]]

			First, the class of permutations is defined, along with how to multiply them and take their inverses. Then, algorithm is spelled out.

			The algorithm yields that their are '''39016857600''' different configurations of the 2x2x3 puzzle. The algorithm was subsequently checked with the Rubik's cube generators given on [http://www.math.toronto.edu/~drorbn/Talks/Mathcamp-0907/NCGE.pdf the handout] and the correct numbers were outputted.

2011-10-11T03:43:25Z

← Older revision		Revision as of 23:43, 10 October 2011
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	This is the Python code used to implement the NCGE algorithm for the 2x2x3 puzzle.		This is the Python code used to implement the NCGE algorithm for the 2x2x3 puzzle.

			[[NCGE Python Code]]
	[[Media:NCGE_code.txt]]

2011-10-11T03:41:12Z

← Older revision		Revision as of 23:41, 10 October 2011
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	This is the Python code used to implement the NCGE algorithm for the 2x2x3 puzzle.		This is the Python code used to implement the NCGE algorithm for the 2x2x3 puzzle.

	[[Media:NCGE_code.txt]]		[[Media:NCGE_code.txt]]

2011-10-11T03:40:59Z

← Older revision		Revision as of 23:40, 10 October 2011
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	[[2x2x3 Permutation Puzzle]]		[[2x2x3 Permutation Puzzle]]


	<nowiki>

	Here are the generators again:		Here are the generators again:

	g1 = [1,2,3,4,12,22,7,8,6,11,21,28,13,14,15,16,17,18,5,10,20,27,23,24,25,26,9,19,29,30,31,32]		g1 = [1,2,3,4,12,22,7,8,6,11,21,28,13,14,15,16,17,18,5,10,20,27,23,24,25,26,9,19,29,30,31,32]

	g2 = [1,2,13,23,5,6,7,4,9,10,11,12,30,14,15,16,17,3,19,20,21,22,29,24,25,26,27,28,8,18,31,32]		g2 = [1,2,13,23,5,6,7,4,9,10,11,12,30,14,15,16,17,3,19,20,21,22,29,24,25,26,27,28,8,18,31,32]

	g3 = [14,24,3,4,5,6,2,8,9,10,11,12,13,32,16,26,1,18,19,20,21,22,23,31,15,25,27,28,29,30,7,17]		g3 = [14,24,3,4,5,6,2,8,9,10,11,12,13,32,16,26,1,18,19,20,21,22,23,31,15,25,27,28,29,30,7,17]

	g4 = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,22,23,24,25,26,17,18,19,20,21,32,31,30,29,28,27]		g4 = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,22,23,24,25,26,17,18,19,20,21,32,31,30,29,28,27]

	</nowiki>

			This is the Python code used to implement the NCGE algorithm for the 2x2x3 puzzle.
			[[Media:NCGE_code.txt]]

2011-10-11T03:35:48Z

← Older revision		Revision as of 23:35, 10 October 2011
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	[[2x2x3 Permutation Puzzle]]		[[2x2x3 Permutation Puzzle]]

			<nowiki>
	Here are the generators again:		Here are the generators again:
	g1 = ~~Perm(~~[1,2,3,4,12,22,7,8,6,11,21,28,13,14,15,16,17,18,5,10,20,27,23,24,25,26,9,19,29,30,31,32])		g1 = [1,2,3,4,12,22,7,8,6,11,21,28,13,14,15,16,17,18,5,10,20,27,23,24,25,26,9,19,29,30,31,32]
	g2 = ~~Perm(~~[1,2,13,23,5,6,7,4,9,10,11,12,30,14,15,16,17,3,19,20,21,22,29,24,25,26,27,28,8,18,31,32])		g2 = [1,2,13,23,5,6,7,4,9,10,11,12,30,14,15,16,17,3,19,20,21,22,29,24,25,26,27,28,8,18,31,32]
	g3 = ~~Perm(~~[14,24,3,4,5,6,2,8,9,10,11,12,13,32,16,26,1,18,19,20,21,22,23,31,15,25,27,28,29,30,7,17])		g3 = [14,24,3,4,5,6,2,8,9,10,11,12,13,32,16,26,1,18,19,20,21,22,23,31,15,25,27,28,29,30,7,17]
	g4 = ~~Perm(~~[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,22,23,24,25,26,17,18,19,20,21,32,31,30,29,28,27])		g4 = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,22,23,24,25,26,17,18,19,20,21,32,31,30,29,28,27]
			</nowiki>

2011-10-11T03:34:42Z

← Older revision		Revision as of 23:34, 10 October 2011
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	The puzzle that I have chosen is a 2x2x3 variant of the Rubik's cube. Below is a sketch of how I have labelled it.		The puzzle that I have chosen is a 2x2x3 variant of the Rubik's cube. Below is a sketch of how I have labelled it along with the permutation generators.

	[[2x2x3 Permutation Puzzle]]		[[2x2x3 Permutation Puzzle]]

			Here are the generators again:
			g1 = Perm([1,2,3,4,12,22,7,8,6,11,21,28,13,14,15,16,17,18,5,10,20,27,23,24,25,26,9,19,29,30,31,32])
			g2 = Perm([1,2,13,23,5,6,7,4,9,10,11,12,30,14,15,16,17,3,19,20,21,22,29,24,25,26,27,28,8,18,31,32])
			g3 = Perm([14,24,3,4,5,6,2,8,9,10,11,12,13,32,16,26,1,18,19,20,21,22,23,31,15,25,27,28,29,30,7,17])
			g4 = Perm([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,22,23,24,25,26,17,18,19,20,21,32,31,30,29,28,27])