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Tuesday, March 28th, 2006  4:32 pm [alun_clewe]

Cumulative Maze
Yeah, okay, it's Tuesday. I know. I'm late again. Sorry. Anyway, I'd said said last week I had two more 45° mazes made that I'd save for this week. But I think instead I'll put up another new kind of maze this week, and save the new 45° mazes for some other week. So...this week's new maze type is called the Cumulative Maze. A Cumulative Maze consists of a grid, some of the cells of which contain symbols. Each turn, you must move a number of cells equal to the number of times you've been on a cell with the same symbol as the cell you're currently in. The current cell counts, and landing on the same cell more than once adds up. For now, you can only move orthogonallythough the concept could certainly be generalized to allow diagonal directions, or other grid types, such as hexagonal. You can jump over a blank cell, but you can't land on it. ( Example behind a cut.Collapse )This type of maze turned out to be much more difficult to design than I expected. (At least, to make small mazes...maybe if I'd used a bigger grid and given myself more room it would have been easier.) I had a couple of 5x5 cumulative mazes made up for this week...and they both turned out to have some drastic short cuts I couldn't get rid of. I finally managed to come up with one that didn't, though I'm still a bit unhappy with it, because I'd tried for a symmetrical arrangement of nonblank cells...but it turned out that whatever symbol I put in the cell east of Start (including a fifth symbol not found elsewhere in the maze), it led to a shorter alternate solution. Ah, well. Here's the maze, anyway: ( Maze behind a cut.Collapse )As an added bonus, here's another LAR maze; refer to this entry for the rules. ( Maze behind a cut.Collapse )I'd had another one of these for this week, too, but I was having a little trouble getting it to work out right, and I'm running late as it is...so I guess that, too, will be saved for some other week.  Monday, March 20th, 2006  11:42 pm [alun_clewe]

45° Mazes
After two consecutive types of "mazes" that kind of stretch the definition, this week's new type of maze is of a more traditional sortthough it still has a set of rules I haven't quite seen used before. Here's a simple example: ( Maze behind a cut.Collapse )And here are the instructions: You start out heading in the direction of the arrow (southeast for all the mazes this week), and continue in a straight line until you hit a square with an octagonal ring in it. At that point, you must make a 45° turnthough it's your choice whether to turn left or right. Then you continue on in a straight line from there until you hit another octagonal ring, and so forth. You're not allowed to leave the gridif you do, you can consider yourself to have hit a dead end. ( Some illustrations of the rules, using the above sample maze, are behind a cut.Collapse )Now that you've seen an example, here are some mazes for you to solve ( , behind a cut.Collapse )I have two more 45° mazes made, but I think I'll save them for next week (particularly since it's late, I still have to run them through the computer to doublecheck them, and I don't feel like doing that right now). So, instead of posting those right now, in my continued attempt to post extra mazes to somewhat compensate for the months of nonupdating I give you two more Jigsaw Maze grids; refer to last week for the rules. (These two mazes use the same fourteen path pieces as last weeks'.) ( Mazes behind a cut.Collapse )  Monday, March 13th, 2006  11:52 pm [alun_clewe]

Jigsaw Mazes (Also, I'm Back!)
Okay, yikes. It's been since November that I haven't posted anything in this community, and October was the last actual maze. Sorry about that; the end of last year was a very difficult time for me, and, well, it took some time to get things back in gear. Anyway, I figure it's well past time I ought to get this community going again. I have a lot of partly finished mazes, or finished but untested, so it's not like I'm out of ideas. Unfortunately, I don't have much time, but I did manage to come up with a new kind of maze for this week. Like the Foursquare Maze a while back, this maybe stretches the definition of a "maze", but, well, the goal is to find a particular path from Start to Finish, so it could qualify... ( More details, and two mazes, behind a cut.Collapse )Speaking of Foursquare Mazes, to start to try to make up for my long absence I want to throw in some extra mazes, so here are a few more of those, too ( , behind a cut. Collapse )Refer back to this entry for the rules. See you next week!  Monday, November 28th, 2005  11:54 pm [alun_clewe]

More Mazelessness
Whoops...I said I was going to finally upload some more mazes last week, didn't I? Sorry. I'm just going through some very hard times right now financially, and I've got a lot on my mind, and unfortunately this community, while I'm still definitely interested in it, isn't exactly my highest priority when I'm worried about where next month's rent is coming from. But I'll try to finally update it next week with some new mazes; sorry for the long delay.  Monday, November 14th, 2005  8:24 pm [alun_clewe]

A Month of Mazeless Mondays
Actually, it's been a little over a month by now, but hey, I wanted to keep the alliteration. Anyway, it's been long enough since I've posted a maze that I thought I should make a post here just to clarify that I have not, in fact, abandoned this community. I've just been really, really busy. I do in fact have a few mazes I am going to post. But, again, I want to run them through a computer test first to make sure I haven't overlooked any drastic short cuts. And I haven't had time to do that. But I will. Probably not tonight, alas, but...well, I'll shoot for next Monday. Yes, that makes four consecutive mazeless weeks, and I'm not happy about that. But, well, I'll try to post five mazes next Monday to make up for it. The type of maze I will post next Monday, incidentally, I have not decided on a name for yet. Perhaps "unison maze". Or maybe by next Monday I'll have come up with a better name for it. Anyway, sorry for the lack of posting. If all goes well, in the near future I should be in a position to have rather more free time, and this shouldn't happen again.  Monday, October 10th, 2005  11:44 pm [alun_clewe]

LAR Maze
Hm. I think I yet again made the mistake of making too long and complicated a solution path, therefore leaving too little room for dead ends and false paths and actually making the maze rather easier than I intended. So I tried to make a second maze with the same rules to correct that, and, um, did the same thing with the second maze too. So, what the hey; these mazes are pretty easy, but maybe later I'll make some other, more difficult mazes using the same rules. Anyway, here are this week's mazes ( , behind a cut.Collapse )And here are the rules: Each space in the mazeexcept the Start and Finish spaceseither is blank or contains either an L, an R, an A. These letters stand for "Left", "Right", and "straight Ahead" (I used "A" instead of "S" to avoid confusion with the Start space), and direct which direction (if any) you have to turn when you get to it. Note that these are relative directions to the way you're facingso, for example, if you enter a space with an "L" on it heading north, you have to leave it heading west; if you enter an "L" space heading west, you leave it heading south; and so on. You can leave a blank space in any direction, except the direction you just came from. If you end up outside the boundaries of the maze, you've hit a dead endyou have to start over. You can leave the Start space in any direction (well, any direction that doesn't take you outside the maze). For example: In the maze on the left, suppose we leave the start space by heading east. This takes us to an R space, so we have to turn right, which means moving south. This takes us to an A space, so we move straight aheadstill south. This brings us to another A space, so it's south once again. Now we're at an R space, so we turn rightwhich means we move west. Now we're at a blank spaceso it's our choice of directions! Unfortunately, no matter which way we go from here (except east, which is illegal because that's the way we just came from), we end up outside of the maze either immediately or after the next moveso it looks like this is a dead end. So apparently on the lefthand maze we have to start out by moving south. You can take it from there. The solutions to the two mazes have 94 and 88 moves, respectively.  Monday, October 3rd, 2005  11:43 pm [alun_clewe]

Foursquare Maze
Hm...calling this a "maze" may be kind of pushing it. Still, the goal is to find a specific path from Start to Finish, so I guess it could qualify. Anyway, here's the maze ( , behind a cut.Collapse )And here are the instructions: Your goal is, as I already mentioned, to find a path from Start to Finish. However, there are some specific criteria the correct path must meet. First, it must follow the dotted blue lines. It may cross the solid black lines, but not retrace them. Likewise, it may cross itself, but not retrace itself. Finally, the completed path, along with the solid black lines, must divide the grid into separate cells each of which contains exactly four squares. In case that last requirement isn't clear, here's an example ( , also behind a cut since it does contain some diagrams.Collapse )  Monday, September 26th, 2005  11:13 pm [alun_clewe]

Equation Mazes
Okay, I confess: I didn't get to verify this one by computer yet. I actually started to, but...the danged program took way too long to run. There probably was a way I could have simplified it, but, well, anyway, it's almost midnight as it is, and I don't want to be late with the maze this time, so...here it is. There may be a shorter alternate solution. If you find one, congratulations. Well, anyway, I'm throwing in two mazes this week, so hopefully at least one of them doesn't have a shortcut solution. So here are the mazes ( , behind a cut.Collapse )Each turn you can jump to another square any distance in any orthogonal direction except the direction you just came from. Your goal is to spell out a series of valid equations; each equation must have two terms on the lefthand side and one term on the right. Thus "15+3=18" and "128*1=128" would be valid equations, for the purposes of solving the maze. "1=1", "171+6=22", and "18/3=4034" would not. When an equation is complete, the result (the number on the righthand side) becomes the first term (on the lefthand side) of the next equation. To finish the maze, you must end an equation on the finish square. Passing through the finish square in the middle of an equation is permissible, but does not solve the maze. For example, you could get started on the first maze like so: From the 1, you can jump east to the 8, then north to any of the division signs, then north again to the 2, west to the equal sign, and south to the 9. You've just spelled out the valid equation 18/2=9. From the 9, you can now go east to the multiplication sign, south to the 3, west to the 7, north to the equal sign, right to the 3 (note that this is the finish square, but we're not at the end of an equation, so the maze isn't solved), south to another 3, and west to yet another, forming 9×37=333, another valid equation. That 333 would then become the first term in the third equationexcept that we can't get to any operators from here, so this turns out to be a dead end. A few nitpicky rules, just to close some possible loopholes: There are no leading zeroes allowed on the numbers. So that means that while you can get to the finish of the first maze quickly by spelling out "18/6=03", the leading zero on the "03" means this isn't a valid solution. Also, the operators count only as operators; you can't use the minus sign to signify a negative number, or the division sign to create a fraction. All the terms in the equations must be positive integers. The intended solutions to both mazes are seven equations long. However, as I said, I didn't get a chance to thoroughly test these mazes for alternate solutions, so I won't promise no shorter solutions (very possibly much shorter solutions) exist.  Tuesday, September 20th, 2005  4:54 pm [alun_clewe]

Common Ground Maze #1
Okay. I didn't have this week's maze up yesterday like I was supposed to. Sorry. The good news is, I already have a maze or two done for next week, so I'm a bit ahead now, and this shouldn't happen again. The maze below is not the maze I had originally planned to have up this week. The maze I had originally planned to have up followed the same rules, but was rather larger, but I was having so much trouble getting it to work that I finally gave up for now and designed a smaller maze with those rules, figuring that would be easier. And it was, but it still wasn't easy. I had actually thought a maze like this would be quite simple and quick to design; I could hardly have been more wrong. Well, anyway, here's the maze ( , behind a cut.Collapse )The rules are as follows: Each move, you can move to an adjacent square in any direction, except the direction you just came from. (Actually, I should clarify that: any orthogonal direction. You can't move diagonally.) On your first move, the square you move to must share at least one symbol with the square you started on. On your second move, the square you move to must share a different symbol with each of the last two squares you were on. And on every move thereafter, the square you move to must share a different symbol with each of the last three squares you were on. So, here's an example: Suppose you start out by moving "east"that square shares a stickfigure symbol with the start square, so that's legal. Now, the square east of here shares a spiral with the square you were just on and a stickfigure symbol with the start square, so you can move east again. But we can't move east again from herethe next square does not share three different symbols with the last three squares. Nor can we move south, for the same reason. So this is a dead end. The shortest solution to this maze has twentysix moves.  Thursday, September 15th, 2005  10:20 pm [alun_clewe]

Another Monday (and Tuesday and Wednesday...) Gone...
All right, I said yesterday that the maze that wasn't up that Monday would be up that night. Clearly, it wasn't. When I said that, I thought the maze was almost done, and that it should be no problem getting it up that night; however... Okay, wait, stop. Actually, even if it had been, I still wouldn't have gotten it up that night, technically; that day ended up being busier than I had expected, and I didn't get time to work on it. However, I would have had it up this morning. Except that when I tried to check it on the computer, I found a major shortcut I'd missed. And when I eliminated that shortcut, I found I'd accidentally eliminated the actual solution instead. And when I patched that I created another short cut...repeat ad nauseam. I think I've really almost got it now. But...at this point I'm thinking rather than put it up four days late, I might as well save it till next Monday. But next week I'll do my best to finish up at least two new mazes...not so I can post them both the following Monday, but so I can have a maze ahead so if I have a busy week and fall behind I have a bit of a buffer. Also, I've been planning to make a Monday Mazes home page where I can put the old mazes in a more convenient place than having to look through all the entries here. I probably won't have that done by this week, but I figured I might as well mention it so there's some relatively good news in this post.  Wednesday, September 14th, 2005  11:13 am [alun_clewe]

Whoops...Late Maze Again
So...uh... last week I said it shouldn't come down again to having to choose between finishing my comic strip or finishing a maze. Well, it kinda did, again. Only this time it's because, well, between Sunday and Monday I ended up doing five strips, four of them in color. Which...took a while. Hence no maze. (And Tuesday...well, there's a reason I planned to post new mazes on Mondays, not Tuesdays or Wednesdays. Though, in retrospect, choosing the same day as my comic site updates probably wasn't the best of ideas. Well, it's alliterative...) I should have this week's maze up tonight, though. It's basically done (has been for well over a week); I just want to doublecheck it for alternate solutions. And I think I'm going to try to get another maze done, while I'm at it, so I can get a week ahead. That way even if something does come up one week that prevents me from getting a maze done in time, I'll have a bit of a buffer so I can still get one up. Oh...this has nothing to do with mazes, but as for the reason I was doing those four extra strips? They were for the Webcomic Hurricane Relief Telethon. Check it out, if you haven't already.  Monday, September 5th, 2005  11:42 pm [alun_clewe]

EPR Maze #1
All right, so, despite my assurances to the contrary, there was no maze up last week. Sorry. This has just been an extremely busy week (and, to tell the truth, after making that post on Wednesday I, um, kept forgetting to finish and post the maze). Hey, at least I managed to get my comics up on time. Apparently when it comes to a choice between the Monday Mazes and the comics, the comics take priority. However, the worst is over as far as the things that have been keeping me busy of late, so hopefully this choice shouldn't come up again. Anyway, I suppose I could put up two mazes this week...but, uh, I won't. I do have one maze for this week, though (the one I'd intended to put up last week), and this time I took the time to doublecheck it by computer to make sure it had a unique solution. ( Maze behind a cut.Collapse )The main thing that requires some explanation is the meaning of the squares with numbers in them. Each of these squares can be replaced with either a horizontal path, like so: or a vertical path, like so: It's your choice which, except that the likenumbered squares must have different paths in them; if one contains a horizontal path, the other must contain a vertical path, and vice versa. Once you have the right paths in the right squares, finding the path through the maze is easybut there's only one way to fill the numbered squares that leaves a valid path through the maze! One other thing that's probably selfexplanatory, but that I'll explicitly go over just in case: Where the paths cross like so: , you can go over or under the crossing, but you can't "jump" it. That is, either of the following are valid moves: This, however, is not: Yeah, this maze is relatively simple; there are only 256 possible choices for how to fill in the squares. I may make a more complicated maze of this type later. As you've probably already seen from the subject, I call this an "EPR maze". Extra points for those who realize why. ;)  Wednesday, August 31st, 2005  6:23 pm [alun_clewe]

Late Maze
Well, there was no "Monday Maze" up on Monday this week. Nor was there one up on Tuesday. I didn't forget this time; I've simply had no time. Between the 17th and the 29th, I was home a grand total of about twelve hours. Part of the problem is I've decided (largely due to 11011110's having found shortcuts in a number of past mazes) that I really need to start doublechecking my mazes more carefully again. So, I do have some new mazes in progress, of some new types that I think are fairly interesting...but I want to carefully doublecheck them and make sure they're free of shorter alternate solutions before I post them. Anyway, combining the time I need to doublecheck my mazes with the time I've been away and unable to do so the last few weeks...well, it's made it quite difficult to get a new maze done (and checked). So...it is now Wednesday, and there may be a maze up later today. But don't necessarily count on it. If not, though, there'll be a maze up tomorrow for sure.  Tuesday, August 23rd, 2005  11:17 pm [alun_clewe]

Inconstant Knight Maze
Yes, this week's maze is up on Tuesday againand very late on Tuesday, at that. No, I didn't forget again. This week, the maze is late for the simple reason that I wasn't home on Monday. I was supposed to bebut I overslept and missed my flight, and got to spend Monday in an airport. Yay. Anyway, here's this week's maze ( , behind a cut.Collapse )It probably goes without saying by this point that you start on the square with the S and your goal is to reach the square with the F. In fact, that so probably goes without saying that from this point on I'm not going to bother to say it anymore. However, there are a few rules this week that are worth saying. For one, you can't land on a square with a red tint. You're free to pass through redtinted squares during your move; you just can't end your move on one. You can only end your move on a square that is pure black or pure white. Yes, that does pretty drastically narrow your choices. So what constitutes a legal move? Well, on your first move, you move like a chess knight: two squares in one direction, and one square in a perpendicular direction. (In this particular maze, that only leaves you one choice for your first movetwo squares south and one square east.) Thereafter, for each move you move X squares in one direction and Y squares in a perpendicular direction, where either X or Y is changed by one from its value in the previous move, while the other stays the same. For instance, since on the first move X=2 and Y=1, on the second move you can choose either X=1 and Y=1, or X=3 and Y=1, or X=2 and Y=0, or X=2 and Y=2. In this particular maze, X=3 and Y=1 won't get you anywhere on your second moveevery square you could reach that way is tinted redbut any of the other three choices works. Suppose you choose X=2 and Y=2. The only square you can reach that way is two squares north and two squares east. From there, you can now choose X=1 and Y=2 or X=3 and Y=2. (Or X=2 and Y=1 or X=2 and Y=3, technically, but these are, of course, equivalent to the other two choices; switching the values of X and Y has no effect.) However, neither of these choices can get you to any square that isn't tinted red. So apparently X=2 and Y=2 was a bad choice as your second move. Hope this makes sense. The intended solution is twentyeight moves long.  Tuesday, August 16th, 2005  6:01 pm [alun_clewe]

TwoTurn Maze
Yes, it's Tuesday. And the thing is, I had this week's maze done yesterdayactually, I had it done Sunday morningbut I, um, kind of forgot to upload it. Anyway, here it is now: ( Maze behind a cut.Collapse )As usual, you start on the node with the S and the goal is to reach the node with the F. The rules this time are as follows: You must go straight every third node. On the other nodes, you must turn. (It's up to you where to start the counting, though...so you can, for example, go straight through the first node you hit, and then turn the next two nodes and go straight after that; or you can turn on the first node, go straight the second, then turn on the next two, etc.) Also, see those triangles over some of the paths? Those are arrows, and they indicate oneway paths; you have to go the direction the arrows are pointing. So, for example: say we start out by heading toward the center of the maze. Now, on our first node (besides the Start node) we have a choice whether we want to turn or not; let's decide to keep going straight. This means at the next nodes we hit we have to turn. Well, we can't turn right at the next node, because that would be going against an arrow, so we have to turn left. And now we have a choice. We can either make a sharp left or a sharp right. (A wide left would take us against another arrow.) Let's take a sharp left. Now, at the node after this, we have to go straight...and this takes us one node away from Start. You should be able to take it from here. (Or take a different path, of course.) The intended solution is thirtyfive moves long.  Monday, August 8th, 2005  10:42 pm [alun_clewe]

ThreeinOne Directional Maze
Whoops...I've had this week's maze done since yesterday morning, but I almost forgot to post it. Anyway, remember what I said last week about making a maze solvable through either last week's ruleset or the one from the week before? Well, I decided to go ahead and make such a maze, and here it is ( , behind a cut.Collapse )I call this a "threeinone directional maze" for a reason. (Um...as opposed to the completely random and arbitrary names I usually give the mazes?) The goal is, of course, to get from one red circle to the other. But you can do so using either the 123 maze rules from last week or the lag maze rules from the week before. So where does the third path come in? Well, for the 123 rules, the solution is different depending on which red circle you start on. (For the lag maze rules, it isn't; you can solve it by the same path regardless of which direction you go.) The thing I'm most dissatisfied about with this maze is the asymmetrical arrangement of the "notches" in the border. I probably could have avoided that had I planned ahead better. But I suppose that's just an aesthetic matter. The intended solutions are 36, 45, and 74 turns long. (I won't bother to say which is whichwell, except that you know the 74move solution has to correspond to the lag maze rules, since the number of turns in any solution to the maze under the 123 maze rules has to be divisible by three (I leave the proof of this as an exercise to the reader ;) ).) But, as usual, there are quite possibly unintended shorter alternate solutions.  Monday, August 1st, 2005  2:00 pm [alun_clewe]

Directional 123 Maze ( Maze behind a cut.Collapse )This maze may look very similar to last week's maze, but the rules are entirely different. It's actually another 123 maze, except that instead of going by color we're going by direction. That is, the rules are as follows: On the first turn, you may move one node in any direction. On the second turn, you must move two nodes in a straight line. The third turn must be three nodes long in a straight line, and then repeat: the fourth turn is one move, the fifth two, and so forth. You can move in the same direction on two successive turns, but you can't go back the way you just came. Of course, you must follow the gray paths; if there aren't gray paths connecting the nodes you want to move across, you can't move there. And, of course, you start at the node with the S, and the goal is to reach the node with the F. Here's an example: Suppose we start by moving one move to the east. Now, we can move east or south; let's pick east again. Since this is our second turn, we have to take two moves (in a straight line). Now, from here we can only move east; we can't move south because we have to take three moves, and we can only move two nodes to the south before running out of gray path. So, all right, we'll move east. From here we can move (one node) either east or south; let's pick east, which takes us to the northeast corner of the maze. Now we can only move south, so let's do it...and, since we took one move last turn, this turn we have to take two moves. Again, we can only move south from where we end up, and this turn we have to take three moves. We're just two nodes away from the finish node now! But this turn we can only make one move. We can move either west or south; let's choose south, toward the finish node. Oops! The next turn, we have to make two moves, but we can't...so we've hit a dead end, just one node from the finish. The intended solution takes thirtynine turns. However, as usual, I won't guarantee there aren't shorter solutions I didn't intend. Hm...regarding the fact that this maze looks so much like last week's: it should be possible to build a single maze that can be solved using either set of rules (with different solutions, naturally). But I guess that's a project for another time... [EDIT: Actually, it turns out this maze can be solved using last week's rules, but the solution isn't very interesting. And last week's maze, alas, has no solution using this week's rules...as is actually quite easy to prove without going to the trouble of trying to solve it (though alas I didn't hit on the proof till after I'd already tried the hard way). [EDIT 2: Last week's maze does, however, have a solution using this week's rules if you start from the Finish and work back to Start...though it's a very short and, again, not very interesting one.]]  Monday, July 25th, 2005  10:57 pm [alun_clewe]

Directional Lag Maze ( Maze behind a cut.Collapse )Here are the rules for this week's maze: Start at the S; you're trying to get to the F (as usual). Each turn, you move along a grey path from the node you're currently on to another node. However, there is a restriction (obviously; otherwise it would be a really easy maze). You may not move in the same direction as you did the turn before last. (It's okay to move in the same direction as you did last turn...just not the same direction as the turn before that.) Also, no backtracking; you can't immediately return back along the same path you just took (though you can return to it at a later point). For example: Suppose you start off by moving south on your first move. Well, that means you'll have to go south on your second move, too. Now, you can't go south on your third move, because you went south two turns ago (on your first move), so you have to go east. Again, you can't go south on your fourth move, because you went south on your second move, but you can go east or north from here. Let's choose east. Whoops! We can't go east again, because we went east two moves ago, but there's no other direction we can go. Looks like we've hit a dead end. The intended solution has fifty moves. However, as usual, I won't swear that a shorter solution doesn't exist.  Monday, July 18th, 2005  9:51 pm [alun_clewe]

Phase Maze #1
I'm not sure what I think of this week's maze. The rules may be more trouble than they're worth. Then again, they may not. Hm. I may experiment more with this later. (Actually, this may be another maze type that lends itself to a Flash implementationnot that I've done any mazes in Flash yet, but I've been meaning to get around to it; in fact, that's the "something different" I've been saying for a while now that I was going to do (but haven't yet gotten around to doing).) ( Maze behind a cut, as usual.Collapse )( ...And the rules.Collapse )  Monday, July 11th, 2005  11:44 pm [alun_clewe]

OneTwoThree Maze #2
All right, I still haven't had a chance to finish any of the more timeconsuming mazes I'm working on, so here's another onetwothree maze. Actually, this could benefit from my spending more time on it, too, I suppose; again, I haven't really had a chance to do any extensive checking, and it wouldn't surprise me at all to find out there are some drastic shortcuts through the maze. But...well...this is all I had time to do this week, and I don't think it's too bad, anyway. ( Maze behind a cut.Collapse )Rules are exactly the same as last week's maze, although we have three colors of paths to deal with now instead of just two. The intended solution is thirtynine moves long, but as I said there may very well be shortcuts that drastically reduce that number. (Whoops...in fact, I just found a twentymove solution. And it's quite possible that yet shorter solutions exist. I've got to start doublechecking these mazes again...) 
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