Tiger in the woods

Can someone please give me some pointers for the 'Tiger in the Woods' puzzles. I have never yet not managed to finish a puzzle in sudoku xtra or sudoku pro but I am struggling with these puzzles and keep coming back to them. Am I missing something really obvious or is there perhaps any omission in the instructions. This will probably turn out to be one of those times where I think how could I possibly have missed something so simple.

I have never posted on here before and would like to say, like many of you, how very much I enjoy Sudoku Xtra and it gets better and better with every edition. I know there were a few 'gremlins' in issue 12 but I still feel it was the best edition yet. I love the wide variety of puzzles and the community section is great. I would reiterate whole heartedly everything Christine says in a previous thread in response to a comment about a mistake-very eloquently put!

Is issue 13 going to be out soon Gareth ?

I had never heard of these puzzles until you mentioned them, then I found Deb Mohanty's puzzles on p46 of Issue 13.

If it makes you feel better, I'm pretty good at most SudokuXtra puzzles, but I did find these puzzles very tricky indeed!

For this puzzle it seems to me you definitely need an eraser, as I suspect a certain amount of trial-and-error is inevitable.

Erasing for me is a practical problem, since I print my puzzles with a laser printer, and an eraser picks up the toner from the page and makes an unholy mess. So I have to redraw these puzzles by hand using a felt-tip pen which doesn't smudge when dry.

Like Nikki, I first of all racked my brain looking for some "trick", in the sense of some rule that allowed you to immediately identify part of the solution. In this I have to admit I failed. In particular there appears to be no obvious way to identify squares that can't be terminals (the start and end squares). All squares are potential terminals (unless, like in the solved example, one is implicit, ie the lower-right corner square).

One useful observation is that you can't turn on an internal square (a square not on an edge and not adjacent to a black square) so for those internal squares that aren't terminal there are only three possible states - passed through horizontally, vertically or both.

Also note that if the path turns in any square, then the direction of that segment of the path is implied (towards the relevant edge or black square).

After much fruitless search for a simple rule that might get me started (one might well exist, but I've not found it) I decided to begin by examining "corner" squares, by which I mean any square with only two possible entry/exit points. If such a square is not terminal then a segment of the path passes through it and the two adjacent squares.

The top-left corner of puzzle 1 is easy to test because if the corner square is terminal then you can see that the other terminal must be one of the two adjacent squares. It was fairly easy to determine that this could not be, so the path passes through the corner. Using the same method I found that the two squares adjacent to the corner can't be terminal either. So I had a definite path segment, 5 squares long, passing through the corner, direction as yet unknown.

An idea for a rough "method" then occurred to me - I would begin by assuming that ALL "corner" squares are NOT terminal. This assumption allows several path segments to be filled in. This would either lead to the solution, or else one of these corner squares must be a terminal, in which case I would then resort to testing each one.

This worked out well for the first two puzzles (although note my postscript below).

I drew up a copy of the puzzle layout and marked with pen all the implied path segments assuming no "corner" squares were terminal. In the first puzzle I was also able to infer the direction for the path segment through the top right corner.

Having a set of path segments, I then tested the end-points of each segment. If one end is a terminal, then the other can't be. Now the pencil and eraser come into use, as I tested each end-point for possibly being a terminal, extending the segment as appropriate when the end-points appeared to be non-terminal.

As I progressed, and the segments became larger, and the occasional segment direction also became implicit, this process became easier until in both of the first two puzzles I found the solution, in which none of these "corner" squares was terminal.

No doubt I will eventually strike one where all of this fails, so one of the "corner" squares must be a terminal, and I will need to to redraw the puzzle and test each corner.

One rule clarification that might be useful is this - when they say that the path can cross over itself, this does NOT apply to the two terminal squares. They must have exactly one entrance or exit.

Hope this helps!

Jim White
Canberra


PS: I rarely consult the solutions section of the magazine. I assume that any solution I arrive at is unique and does not need checking. Imagine my surprise when I found that my solution to the second puzzle is not the same as that given!

Mine is definitely valid, and so is the one given, so we have a non-unique solution, ie. an error. I'll report this in a separate post.

Interestingly, the given solution has both terminals as corner squares. If I'd tested all corner squares as terminals BEFORE assuming they weren't, I'd never have known there was a problem.

Nikki, check out davmillar's reply to my post regarding the multiple-solutions here

You'll be pleased to know there were some "missing" rules, although on closer inspection I'm not sure that they give rise to any radically different strategy.

Note that the first of the two missing rules is the one I suggested above was probably true anyway - the path can't re-cross either of the two terminal squares.

The second one is a new condition, that the end-point has to be at a square that would involve a turn were it not the final end-point.

I don't think that changes the general approach that I described above, but it does make the process somewhat easier.

Given a partial path segment, we want to test whether either end of it is terminal. Since it's usually much easier to test a square for being a start-point than to test it for being an end-point, knowing that many squares (eg. what I called "internal" squares above) can't be end-points certainly helps.



Edited 3 time(s). Last edit at 01/23/2011 05:49PM by Mathimagics.

Oh wow, thank you so much for your very detailed response. I havn't had a chance to look at it in detail yet but good to know it wasn't just me being dense and losing my puzzle mind. I suspect these puzzles may involve too much trial and error for my liking - being a bit of a sudoku purist - but i'll have another go with the new info. Thanks again for your help

Hi Nikki, nothing to add to this topic really except to say I've had a go at Tiger in the Woods too and also drew a blank, but might have another look since Mathimagics has taken the trouble to explain in so much detail!

You must be a really great puzzler if that is the only thing in Xtra which has troubled you! I usually manage to complete about three quarters of the puzzles, but there are always a few which I can't do! (Am going off to start a new thread on Krypto Kakuro!)

Just wanted to say thank you for seconding my thoughts on the magazine in a previous thread. Do keep posting! We could do with a bit more discussion going on here!

I based the instructions for this puzzle (Tiger in the Woods) on those given in the 2009 LMI (Indian) puzzle championships, where this rule about finishing only on what would be a turn square wasn't stated. It does at least make the puzzle a bit easier when you add that additional restriction in!

I do apologise for this confusion, and I should have made sure I'd checked the instructions with the puzzle's author directly.

I will be updating the issue 12 PDF again at the same time as issue 13 is available (in the next couple of days).



Edited 5 time(s). Last edit at 01/24/2011 06:48PM by gareth.

Hi Christine, I wouldn't say 'Tiger in the Woods' is the only puzzle that has troubled me but it is the first one that has beaten me and which I needed help with. I probably have too much free time and a slightly 'obsessive' mentality but I find usually if you keep working on something for long enough it eventually falls into place.

I will try and post more often. It would be good to discuss my 'hobby' with more like minded people.

I am sooooo looking forward to issue 13 !!

Quote
Nikki
I probably have too much free time and a slightly 'obsessive' mentality but I find usually if you keep working on something for long enough it eventually falls into place.

Um, er, snap!

We don't do "hobbies", we just pursue obessions!

Aaaaarrrrrgggghhhhh...I think I am just about ready to admit defeat. I cannot get beyond a couple of short pieces of path in any of these puzzles, even with the extra instructions, and it is driving me nuts! Either there is a really serious amount of trial and error or I have been beaten!

If this is me being super dim I wonder if Gareth, Davmillar or Jim would be kind enough to post a step by step walk through of the first puzzle for me. I know Jim sort of already did but that was before the missing instruction and making assumptions that turned out not to be the case.

If in fact a lot of trial and error is needed rather than logic then I would question whether that is the right type of puzzle for a [BRILLIANT] sudoku and logic puzzle magazine. [Sorry-didn't mean for that to sound grumpy!]

Please put me out of my misery!

Hi Nikki,

My name is Deb, and I'm the author of these puzzles.
Firstly, I agree with you that this puzzle type is not a completely logical puzzle. In a Sudoku or in a Slither Link, you can deduce all the steps by logic. But this puzzle needs bit of visualization. Something that a puzzle like Number Link (aka ABC Connection) needs.

I've attached steps for the first puzzle. Please have a look at it, and post any questions you may have.

Deb

Edit : A modified version of this document is attached in a newer post.



Edited 1 time(s). Last edit at 02/03/2011 03:59AM by debmohanty.

Oh thanks so much Deb. I've had a quick look and that looks great-just what I needed. You've put a lot of effort into that and it looks very clear and easy to follow. I don't have much free time in next few days but will study it as soon as I can and let you know how I get on.

Nikki

Some puzzles arouse strong emotions, and Deb's example of Numberlink is spot on. Some people can't bear them, and I must admit that when I first tried Numberlink I thought they were ridiculous. However with experience I learnt to visualise them much more easily, and my Numberlink intuition grew to the point where they are now one of my absolute favourite puzzles of all. Whether that will happen with Tiger in the Woods I don't know, but they are similar and I suspect a lot of the same organic "feeling" would grow if you solved enough of these. So in my opinion they're definitely entirely valid puzzles to include, and I'm very grateful to Deb for generously contributing them to the magazine.

In any case I actually think that any puzzle that engenders discussion is a huge success, no matter what! As a puzzle author I can say without doubt that any feedback is better than no feedback - that's how we can work out where the best place to focus our efforts is.

PS And I thoroughly recommend Deb's excellent work-through - it's awesome!

Oh gosh-I do hope my comments didn't sound offensive-I certainly didn't mean them to. I really wish I hadn't put that comment about questioning the type of puzzle-sorry Deb and Gareth! I was just getting very frustrated at my inability even to get started on these puzzles. When I go through Deb's fab work-through I hope it will fall into place.

I actually do like Numberlink [although it took me a while to be comfortable with a slightly different mental approach] and I can see there is a difference between visualisation and trial and error. The comparison with Numberlink will probably help me to crack these puzzles.

Deb I hope you will take it as a compliment that you have introduced puzzles that have generated discussion and more than a little frustration!

Well I can't speak for anyone else but I certainly wasn't offended! Like I said, it's brilliant to see people discussing the puzzles!

No problem, Nikki. I can understand your frustration. I had similar feeling when I first saw the puzzles (in WPC 2005), it definitely took me more than ideal time to realize how to approach the puzzles.

PS: With time-zone differences, my replies may seem bit delayed. But I'm trying to visit this forum as often as I can.

Ok Deb, thanks to your great work-through I think the fog is starting to clear, but I still need more help. With the information that that the path has to start in row 4 I can then go on to complete the puzzle. However I still cannot come to that first conclusion on my own in the first place, and that of course is crucial as you cannot carry on without it. I am still struggling to find the first moves in the other puzzles, but I think I should still concentrate on the first one for now.

It would appear visualisation is not my strong point! Is there any more help you can give me, maybe take the work-through back a stage to show how to establish that first point.

Incidentally I was able to establish from the start that path has to travel through two sections i.e. R1C1 R1C2 R1C3 R2C1 and R3C1, and R2C6 R3C6 and R4C6, but I am not sure how important this is at the start as you do not refer to these cells until much later on.

I am sorry to be such a pain with this but I cannot let it go until I have cracked it!

I think the path has to start either in row 4 or the bottom three squares of column 5 - if it doesn't then it can't visit R4C5, since there are no places it can turn to reach this square. I don't see how you eliminate column 5 as a possibility right at the start, but for the purpose of the next step of the walk through it doesn't matter because you have proven where the start isn't (i.e. anywhere else).

Hi Nikki,
I definitely missed a point there. Thanks Gareth for catching.

To visit R4C4, the path must start in Row4, OR it can start at R5C5/R6C5 and move upwards to R4C5, and then taking a left.
The document misses why R5C5 or R6C5 are eliminited from the beginning.

As Gareth mentioned, it is not completely necessary to rule out R5C5 / R6C5 as starting points. I've modified the document not to exclude them as starting points.

However, it is also clear that none of them can be starting points.

R5C5 :
Focusing on R5C4 - The only way this cell can be visited when the path comes from R5C1 and moving to R5C6.
This path passes through R5C5, and hence R5C5 can't be the starting point.

R6C5 :
Focusing on R6C2 and R6C4 - It should be apparent that the path must come from R6C6 and moving to R6C2. This path passes through R6C5 and hence R6C5 can't be the starting point.
[ If the path comes from R1C3 hitting R6C3, then one of the two cells will remain unvisited. ]

Deb

I've just had the time to take another look at the Tiger in the Woods puzzles and here's my honest opinion: they're not that hard. I thought they were all really enjoyable puzzles that just needed a different mindset to solve.

I solved each one in about a minute or so, using no complex logic at all. The secret is to solve them very differently to a regular logic puzzle. Instead of starting with things you know to be true, in this puzzle you must start with things that are only likely to be true. So what I did was I drew in lightly all of the obvious corner and block turns and extended them where they must go. I carried on drawing lines where they had to reflect in order to reach areas, and in every puzzle I ended up after this with one or two squares (or in one case areas) which weren't reached by any reflection. I then knew this was where the solution path started, and by looking at my sketched lines that were already drawn I could see how big chunks of the solution must go. I also in some cases knew from simple inspection which way the path must be travelled in order for a reflection to be used, which helped limit the options too. Then it was quick experimentation with different moves from the starting point until I found one which worked. This whole experimental process took around a minute per puzzle, and in fact the larger ones were no harder than the smaller ones using this system.

So overall I thought they were brilliant puzzles. Harking back to an earlier point, however, this logic does require you to need to know that the line ends at a solid wall. Without this the level of uncertainty is much greater (and indeed the solution is not necessarily unique as pointed out before).



Edited 4 time(s). Last edit at 03/16/2011 02:33PM by gareth.