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Philmac
Joined: 04 Aug 2005
Posts: 16
Location: Cheshire, England
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 Posted: Wed Aug 24, 2005 10:08 am Post subject: order of steps in the solution |
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I am intrigued to know whether there is an order to the solution of a puzzle.
Clearly towards the end the answer is NO as there are many different ways to fill in the EASY remaining blanks. Similarly at the beginning, the fill-ins tend to be fairly independent (or at least that seems to be how I find them; e.g. I do maybe the 4's, then the 5's but I could have done them in reverse order). But I get the 'sense' that at the tricky middle stage there may be very few possible routes through (maybe only one). Of course the latter requires that puzzlers have reached the same grid of numbers.
What triggers my curiosity is that when people celebrate their joy of solving a puzzle and thank the compiler, have the solver and the compiler actually been on the same journey (at least through the tricky middle part) or are they possibly journeying along completely different routes? I haven't seen any posts along the lines of "r4c5 was really tricky and marked the breakthrough" |
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samgj
Site Admin
Joined: 17 Jul 2005
Posts: 106
Location: Cambridge
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| Posted: Wed Aug 24, 2005 7:12 pm Post subject: Re: order of steps in the solution |
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| Philmac wrote: | I am intrigued to know whether there is an order to the solution of a puzzle.
<snip>
What triggers my curiosity is that when people celebrate their joy of solving a puzzle and thank the compiler, have the solver and the compiler actually been on the same journey (at least through the tricky middle part) or are they possibly journeying along completely different routes?" |
Hello Philmac
I think the answer is a nearly yes. To start with there is sometimes only one possible move, which leads to only one more. Clearly there may be more than one, and there are then several short parallel paths, but they probably come back together just before a difficult step. This is because a difficult puzzle is often characterised by only one or two difficult steps in the middle somewhere. These will be done in the same order by nearly everyone who does the puzzle I think. Certainly I get email from several people stuck in the same place on the same puzzle. Of course, some people may notice the difficult step a little earlier in the proceedings, before they have perhaps completed all of the easier moves leading up to it.
A slightly different way of looking at this is that, based on a ordering of how hard each logical step is, there is very likely to be a single easiest path though. A lot of people won't deviate far from this easiest path, but some of course will.
This doesn't necessarily apply to the order the computer will fill in squares though -- because it has a full range of logic moves to apply at each step, it may do a tough step before an easy one. (Actually, the hint option in "draw" is programmed to try easy steps first and then the hard ones, but sometimes it still seems to come up with moves that are logical and possible, but not the first intuitive thing that a human would do.)
Ramble, ramble, I hope at least some of that is useful.
Sam |
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Philmac
Joined: 04 Aug 2005
Posts: 16
Location: Cheshire, England
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| Posted: Wed Aug 24, 2005 8:58 pm Post subject: order of steps |
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| That's very helpful coming from an expert. It does more or less confirm what I had suspected - interesting though, and thanks for taking the time to post such a detailed response. |
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