Longest road - Revision history

Oscarlevin at 01:29, 15 July 2013

2013-07-15T01:29:36Z

← Older revision		Revision as of 19:29, 14 July 2013
Line 8:		Line 8:

	{{Hint\| You could color the intersections in a checkerboard pattern. What can you say about the parity of the length of any path?}}		{{Hint\| You could color the intersections in a checkerboard pattern. What can you say about the parity of the length of any path?}}

	{{Answer \| 142 blocks}}		{{Answer \| 142 blocks}}

Oscarlevin at 23:01, 14 July 2013

2013-07-14T23:01:47Z

← Older revision		Revision as of 17:01, 14 July 2013
Line 14:		Line 14:
	==See also==		==See also==

	[[~~Checker board~~ and dominoes]]		[[Checkerboard and dominoes]]

	[[Checkerboard cut-up]]		[[Checkerboard cut-up]]

Oscarlevin at 22:54, 14 July 2013

2013-07-14T22:54:38Z

← Older revision		Revision as of 16:54, 14 July 2013
Line 1:		Line 1:
			==Puzzle==

	Grid-town USA, in addition to its excellent donut shops, is known for its precisely laid out grid of streets and avenues. The town has 12 avenues running east/west, creatively named 1st, 2nd, etc. There are also exactly 12 streets (running north/south) also named 1st, 2nd, 3rd, and so on.		Grid-town USA, in addition to its excellent donut shops, is known for its precisely laid out grid of streets and avenues. The town has 12 avenues running east/west, creatively named 1st, 2nd, etc. There are also exactly 12 streets (running north/south) also named 1st, 2nd, 3rd, and so on.

	Suppose you are a cab driver in Grid-town. You pick up your fair at the corner of 1st and 1st and are instructed to travel all the way across town, to 12th and 12th. Of course you want to maximize the length of the trip. However, your passenger will get suspicious if you leave town or cross through any intersection more than once. What is the longest path you can take?		Suppose you are a cab driver in Grid-town. You pick up your fair at the corner of 1st and 1st and are instructed to travel all the way across town, to 12th and 12th. Of course you want to maximize the length of the trip. However, your passenger will get suspicious if you leave town or cross through any intersection more than once. What is the longest path you can take?

			==Help==

	{{Hint\| You could color the intersections in a checkerboard pattern. What can you say about the parity of the length of any path?}}		{{Hint\| You could color the intersections in a checkerboard pattern. What can you say about the parity of the length of any path?}}
Line 8:		Line 12:
	{{Needs solution}}		{{Needs solution}}

	[[~~Category:New~~]]		==See also==
	[[~~Category:MCP~~]]
			[[Checker board and dominoes]]

			[[Checkerboard cut-up]]

	[[Category:Combinatorics]]		[[Category:Combinatorics]]
	[[Category:Parity]]		[[Category:Parity]]
	[[Category:Graph theory]]		[[Category:Graph theory]]

Oscarlevin at 01:49, 7 July 2013

2013-07-07T01:49:55Z

← Older revision		Revision as of 19:49, 6 July 2013
Line 4:		Line 4:

	{{Hint\| You could color the intersections in a checkerboard pattern. What can you say about the parity of the length of any path?}}		{{Hint\| You could color the intersections in a checkerboard pattern. What can you say about the parity of the length of any path?}}

	{{Answer \| 142 blocks}}		{{Answer \| 142 blocks}}

Oscarlevin at 23:22, 28 June 2013

2013-06-28T23:22:23Z

← Older revision		Revision as of 17:22, 28 June 2013
Line 5:		Line 5:
	{{Hint\| You could color the intersections in a checkerboard pattern. What can you say about the parity of the length of any path?}}		{{Hint\| You could color the intersections in a checkerboard pattern. What can you say about the parity of the length of any path?}}

	{{Answer\| 142 blocks}}		{{Answer \| 142 blocks}}

	{{Needs solution}}		{{Needs solution}}

Oscarlevin: Created page with "Grid-town USA, in addition to its excellent donut shops, is known for its precisely laid out grid of streets and avenues. The town has 12 avenues running east/west, creativel..."

2013-03-17T20:56:10Z

Created page with "Grid-town USA, in addition to its excellent donut shops, is known for its precisely laid out grid of streets and avenues. The town has 12 avenues running east/west, creativel..."

New page

Grid-town USA, in addition to its excellent donut shops, is known for its precisely laid out grid of streets and avenues. The town has 12 avenues running east/west, creatively named 1st, 2nd, etc. There are also exactly 12 streets (running north/south) also named 1st, 2nd, 3rd, and so on.

Suppose you are a cab driver in Grid-town. You pick up your fair at the corner of 1st and 1st and are instructed to travel all the way across town, to 12th and 12th. Of course you want to maximize the length of the trip. However, your passenger will get suspicious if you leave town or cross through any intersection more than once. What is the longest path you can take?

{{Hint| You could color the intersections in a checkerboard pattern. What can you say about the parity of the length of any path?}}

{{Answer| 142 blocks}}

{{Needs solution}}

[[Category:New]]
[[Category:MCP]]
[[Category:Combinatorics]]
[[Category:Parity]]
[[Category:Graph theory]]