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Topic: Canterbury Puzzle 1 (Read 765 times) |
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rloginunix
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Canterbury Puzzle 1
« on: May 30th, 2015, 6:25pm » |
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The Travelling Salesperson Puzzle.
It is well known that Geoffrey Chaucer wrote a number of Canterbury Tales at the end of the 14th century. It is less well known that Chaucer could do some mean math and a recently discovered set of Canterbury Puzzles is thought to belong to his pen. Get a free lunch at Tabard/Talbot Inn (London, UK) for solving any puzzle of the set. Here is one.
Once upon a time there lived a shrewd but unscrupulous chap who made his living by roaming the English countryside selling the papal indulgences (pardons) to the good citizens of Albion. The lad managed to visit every town of 64 only once travelling in 15 straight lines only:
He started from the Blue Town knowing ahead of time that there is no path between the two Red Towns. How did he do it?
If you can not submit a pictorial answer do it algebraically - number the towns by row and column starting each at 1. Your solution must begin with r7c3.
(I'm translating all of this. If anything is off I hope rmsgrey will keep me honest)
How many solutions did you find? I've got 3 - two ending at r7c2, one at r8c1.
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towr
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You missed at least another ending at r8c1
Now to see if there's any more.
[edit]I've got nine so far, still always ending at the same two spots.[/edit]
[edit2]wow, I'm still missing a lot; there's at least 13 solutions. 4x3+1[/edit2]
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| « Last Edit: May 31st, 2015, 11:48am by towr » |
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rloginunix
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Re: Canterbury Puzzle 1
« Reply #2 on: Jun 1st, 2015, 6:19pm » |
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Yes, you are right. A linear combination of the portions of the primitive solutions, good idea.
I was wondering why this 1907 book by H. E. Dudeney listed only one solution for this puzzle - the one marked as +1 in your drawing.
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Grimbal
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Re: Canterbury Puzzle 1
« Reply #3 on: Jun 8th, 2015, 4:57am » |
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I have one more. Take towr's 13th and do the last loop (last 7 moves) in reverse.
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towr
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Re: Canterbury Puzzle 1
« Reply #4 on: Jun 8th, 2015, 8:54am » |
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Nice find, I'm embarrassed to have missed it. (Considering that the exact same change in direction/connection happens in the first block of 4 half-solutions)
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rloginunix
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Re: Canterbury Puzzle 1
« Reply #5 on: Jun 8th, 2015, 10:17am » |
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If anyone takes home the embarrassment prize it must be me, for doing a half-a.. job.
Documenting Grimbal's find.
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Grimbal
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I arrive at 18  .
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| « Last Edit: Jun 12th, 2015, 12:13pm by Grimbal » |
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towr
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Re: Canterbury Puzzle 1
« Reply #7 on: Jun 11th, 2015, 11:24pm » |
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I've run an exhaustive search with a python script, and suffice it to say that Grimbal's found all solutions.
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