Project Euler/15 - Revision history

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2019-03-18T05:30:54Z

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2018-01-08T08:18:44Z

4 Dimensional Lattice Example

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 Let's look at the example of a traversal of a 4D lattice, which we can think of as the evolution of a 3D traversal in time
 (a step in the fourth dimension would represent a "pause" in the 3D traversal).
 Consider the traversal of a cube with dimensions <math>3 \times 4 \times 5 \times 3</math>. Then
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 [[Image:Mathematica_LatticePermutations.png|800px]]
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2018-01-08T08:10:53Z

← Older revision		Revision as of 08:10, 8 January 2018
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	~~Also see:~~		[[Project Euler/172]]
	* [[Project Euler/172]]
	* [[AOCP/Multisets]]		[[AOCP/Multisets]]
	* [[AOCP/Multinomial Coefficients]]
	* Shortest Lattice Paths and Multiset Permutations: https://charlesreid1.github.io/shortest-lattice-paths-and-multiset-permutations.html		[[AOCP/Multinomial Coefficients]]

			Blog post: Shortest Lattice Paths and Multiset Permutations: https://charlesreid1.github.io/shortest-lattice-paths-and-multiset-permutations.html

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2018-01-08T08:04:12Z

← Older revision		Revision as of 08:04, 8 January 2018
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	* [[Project Euler/172]]		* [[Project Euler/172]]
	* [[AOCP/Multisets]]		* [[AOCP/Multisets]]
			* [[AOCP/Multinomial Coefficients]]
	* Shortest Lattice Paths and Multiset Permutations: https://charlesreid1.github.io/shortest-lattice-paths-and-multiset-permutations.html		* Shortest Lattice Paths and Multiset Permutations: https://charlesreid1.github.io/shortest-lattice-paths-and-multiset-permutations.html

2018-01-08T08:03:11Z

← Older revision		Revision as of 08:03, 8 January 2018
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	* [[Project Euler/172]]		* [[Project Euler/172]]
	* [[AOCP/Multisets]]		* [[AOCP/Multisets]]
			* Shortest Lattice Paths and Multiset Permutations: https://charlesreid1.github.io/shortest-lattice-paths-and-multiset-permutations.html

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2018-01-08T08:02:53Z

Flags

2017-07-18T11:26:51Z

2017-07-18T09:04:52Z

← Older revision		Revision as of 09:04, 18 July 2017
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	To formulate our problem in these terms, we can think of "distributing" our down moves as we move right through the lattice. On the 20x20 grid, we are going to make 20 right moves, and we can distribute our 20 down moves at any of 21 possible locations (columns of points on the lattice).		To formulate our problem in these terms, we can think of "distributing" our down moves as we move right through the lattice. On the 20x20 grid, we are going to make 20 right moves, and we can distribute our 20 down moves at any of 21 possible locations (columns of points on the lattice).

	Thus, our n items, the 20 down moves, are being placed between ~~the~~		Thus, our n items, the 20 down moves, are being placed between the 20 right moves, which are the 20 bars that create 21 bins (21 locations to place the down moves).
	the 20 right moves, which are the 20 bars that create 21 bins (21 locations to place the down moves).

	Considering the smaller 2x2 example, and replacing bars with R, we have, for a 2x2 lattice, six possibilities:		Considering the smaller 2x2 example, and replacing bars with R, we have, for a 2x2 lattice, six possibilities:

2017-07-18T08:50:22Z

Number of Paths Thru Lattices of Arbitrary Size

2017-07-18T08:49:24Z