At http://home.att.net/~robtabbott/theseus.html, you will find an outstanding computer game, written in Java but masquerading as a maze puzzle. It's more like a deadly version of PacMan. After trying for a couple of weeks to solve it, I ordered Robert Abbott's book, Supermazes and got the solution. My only regret is that I could not get hints before I gave in. I probably could have solved it, had I only be able to confirm I was on the right track, and a couple of steps away from the solution. Try it. You'll hate me.
Web
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Yes, this is a fantastic maze. It usually takes about a week to solve it. That makes about one day per minotaur trap. An easier maze by Abbott can be found at my site as the Puzzle of the Week at www.mathpuzzle.com.
In article <01be06ac$07597f80$37158...@bryanw-w95.tritech.com>, "Bryan Wolf" <bryanwRemoveForNoS...@tritech.com> wrote:
> webster2...@my-dejanews.com wrote in article > <71gav3$hl...@nnrp1.dejanews.com>... > > At http://home.att.net/~robtabbott/theseus.html, you will find an > outstanding > ... > > ... Try it. You'll hate me.
> You're right. I do. :-) > Give me a hint, at least. Does the solution begin with the sequence below? > <pseudospoiler follows>
> U,D,R,L = Up, Down, Right, Left
> UURRRDDL possibly followed with DDDDRRU
I think you meant DDDDRRRU for the second bit. Follow that with UUUURRUURRRURRRL and you get the minotaur in another trap. After that I'm currently stuck.
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In article <01be06ac$07597f80$37158...@bryanw-w95.tritech.com>, "Bryan Wolf" <bryanwRemoveForNoS...@tritech.com> wrote:
> webster2...@my-dejanews.com wrote in article > <71gav3$hl...@nnrp1.dejanews.com>... > > At http://home.att.net/~robtabbott/theseus.html, you will find an > outstanding > ... > > ... Try it. You'll hate me.
> You're right. I do. :-)
Got it ! Spoiler space follows . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . UURRRDDL (trapped minotaur) DDDDRRRUUUUURRUURRRURRRLL (trapped minotaur) LDLLLDDDDDDDRRRRRRL (pause one movement here or go left then right) LUUULLLLUUUUUL (trapped minotaur) LDDDDDDDDRRRRRRRU (got the minotaur where you want it) UUUUURUR (exit)
-----------== Posted via Deja News, The Discussion Network ==---------- http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own
> webster2...@my-dejanews.com wrote in message > <71gav3$hl...@nnrp1.dejanews.com>... > >At http://home.att.net/~robtabbott/theseus.html, you will find an > outstanding > >computer game, written in Java but masquerading as a maze puzzle.
> Yes, this is a fantastic maze. It usually takes about a week to solve it. > That makes about one day per minotaur trap. An easier maze by Abbott can be > found at my site as the Puzzle of the Week at www.mathpuzzle.com.
This was a fun game. I thought I had a good start, but I guess it was not to be. I was trying:
UURRUULLD RRRRDDRDR
this would semi-trap the Minotaur and allow you to get a head-start but I couldn't get past that. I did resort to the hints for the first 3 traps. The third trap's timing is pretty tough!
>webster2...@my-dejanews.com wrote in message ><71gav3$hl...@nnrp1.dejanews.com>... >>At http://home.att.net/~robtabbott/theseus.html, you will find an >outstanding >>computer game, written in Java but masquerading as a maze puzzle. >Yes, this is a fantastic maze. It usually takes about a week to solve it.
ObPuzzle: How is such an assessment made? Did lots of people get this puzzle in some sort of scientifically controll-ed environment? Is this just some vague anecdotal statement based on friends' comments, all of whom no doubt must be pretty interested in puzzles to even attempt the maze to begin with? Or maybe "I solved it in one day, and most people are seven times more stupid than I am ... " :-)
For the record, my history with the maze is: 1992 -- saw it in "Mad Mazes," said "This is too tedious," promptly ignored it. Yesterday -- saw the URL above, played with the maze for about an hour, thought I made significant progress. Then I realized that I had gone into a "dead end" and didn't make as much progress as I thought. Got frustrated and stopped playing. Today -- Saw Ed Pegg's post above, went back to the URL, solved the maze. Real cool -- but thought it was rather annoying that certain regions of the maze were irrelevant to the solution. (Kinda like the distractor pieces in a good chess problem.) Then posted this message.
Net time: 90 minutes, two days, or 6 years, depending on how you count the breaks. :-) -- Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- You too may suffer from cellular cyclosis -- ask your doctor!
> Yes, this is a fantastic maze. It usually takes about a week to solve it. > That makes about one day per minotaur trap. An easier maze by Abbott can be > found at my site as the Puzzle of the Week at www.mathpuzzle.com.
> --Ed Pegg Jr.
Agreed. I woke up Sunday with a headache after a Halloween party and started playing with the dammed thing. After being chased here and there and wasting half the day on it, I managed to convince myself there was no solution (I was following one of the blind alleys). So I actually wrote a program to see if there was a solution. The program had a bit more patience than I did and took about one second to report there WAS one. Armed with that knowledge I went back and found it.
Interestingly, the program dodged the blind alley initially but managed to explore it from a different direction before coming back and finding the answer. (If you've wasted a week to solve this you'll know what I'm talking about...)
If you are interested or really must cheat, the program is below.
PUZZLE.
This program (as I first ran it) has a bug in it such that it doesnt quite comply with the conditions of the maze. Funnily enough, it finds a solution anyway. So one of the conditions is unnecessary.
What is missing from the program?
Philosophically, the fact that this condition is unneccessary I find to be a very minor blemish on the solution, (though of course it adds to the difficulty of solving it).
It should possible to come up with another maze (as fiendish as this one) but having the extra condition necessary for finding a solution!
SPOILER java program... should be easy to convert to C/C++
public class theseus { static boolean a[][], U[], D[], R[], L[];
public static boolean TestMove(int i, int j) { int ii, k=2; while (k-- >0) { // Move the Minotaur twice... if ((ii = (i%14 - j%14))<0 && L[j]) j--; else if (ii>0 && R[j]) j++; else if ((ii=(i/14-j/14))<0 && D[j]) j -= 14; else if (ii>0 && U[j]) j += 14; if (i==j) return false; // Caught } if (a[i][j]) return false; // We've already been here System.out.println(String.valueOf(i)+" "+String.valueOf(j)); if (i==111) return true; // Made it! a[i][j] = true; // Mark position visited if (R[i]) if (TestMove(i+1, j)) return true; // Check right.. if (L[i]) if (TestMove(i-1, j)) return true; // left if (U[i]) if (TestMove(i+14, j)) return true; //etc if (D[i]) if (TestMove(i-14, j)) return true; return false; // No luck }
public static void main(String[] args) { a = new boolean[126][126]; D = new boolean[126]; .... // Stuff setting up U, L, D, R arrays deleted .... // Cells are numbered 0-125 starting in the lower left // corner and running left to right. // The U, D, L, R arrays specify the maze by saying // whether it is possible to move in that direction from // a particular cell, eg U[0]=true, L[0]=false // The a[][] array stores visited positions. // If you REALLY must cheat, just define the U,L,D,R arrays // and compile and run the program. // It should also work with any other maze subject to the // same rules. ....
Wei-Hwa Huang <whu...@ugcs.caltech.edu> wrote: >Today -- Saw Ed Pegg's post above, went back to the URL, solved the > maze. Real cool -- but thought it was rather annoying that > certain regions of the maze were irrelevant to the solution. > (Kinda like the distractor pieces in a good chess problem.)
"Distractor pieces" went out of fashion about a century ago -- nowadays every piece and pawn in a good chess problem must have some specific function (i.e. the problem must become unsound or lose thematic content if any one or more pieces is/are deleted).
Bryan Wolf <bryanwRemoveForNoS...@tritech.com> wrote: > webster2...@my-dejanews.com wrote in article > <71gav3$hl...@nnrp1.dejanews.com>... >> At http://home.att.net/~robtabbott/theseus.html, you will find an > outstanding > ... >> ... Try it. You'll hate me.
well, the maze is quite difficult the first time you try it but once you have the intuition it becomes really simple to trap the minotaur and get away. It took me about 1 hour to solve the maze. I thought it was a lot, but after the reading the rest of the mails i was pretty happy with myself :-)
i am not including the solution so as not to spoil the fun of other readers, but if any of you want the solution mail me and ill be glad to send it to you
sid
> U,D,R,L = Up, Down, Right, Left > UURRRDDL possibly followed with DDDDRRU
--
******************************************************************* * * * Abscence is to Love what wind is to fire - it puts off the * * small and kindles the great * * * *******************************************************************
Siddhartha Mathur wrote in message <71ot4j$s3...@news.cs.ucla.edu>... > well, the maze is quite difficult the first time you try > it but once you have the intuition it becomes really simple > to trap the minotaur and get away. It took me about 1 hour > to solve the maze. I thought it was a lot, but after the > reading the rest of the mails i was pretty happy with myself :-)
> i am not including the solution so as not to spoil the fun > of other readers, but if any of you want the solution mail > me and ill be glad to send it to you
> sid
This was pretty much my experience. After the first insight, I pretty much knew what I wanted to do at each successive step and just had to figure out how to get there. Still, a very nice puzzle.
Noam D. Elkies <elk...@mminotaurath.harvard.edu> writes:
>Wei-Hwa Huang <whu...@ugcs.caltech.edu> wrote: >>Today -- Saw Ed Pegg's post above, went back to the URL, solved the >> maze. Real cool -- but thought it was rather annoying that >> certain regions of the maze were irrelevant to the solution. >> (Kinda like the distractor pieces in a good chess problem.) > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >"Distractor pieces" went out of fashion about a century ago -- >nowadays every piece and pawn in a good chess problem must have >some specific function (i.e. the problem must become unsound or >lose thematic content if any one or more pieces is/are deleted).
A whole century? Wasn't Sam Loyd composing chess puzzles into the 1900's? Or was that, like Raymond Smullyan's retro puzzles, "far behind what the REAL puzzle-makers were doing"?
-- Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- You too may suffer from cellular cyclosis -- ask your doctor!
Wei-Hwa Huang <whu...@ugcs.caltech.edu> wrote: >Noam D. Elkies <elk...@mminotaurath.harvard.edu> writes: >>Wei-Hwa Huang <whu...@ugcs.caltech.edu> wrote: >>>Today -- Saw Ed Pegg's post above, went back to the URL, solved the >>> maze. Real cool -- but thought it was rather annoying that >>> certain regions of the maze were irrelevant to the solution. >>> (Kinda like the distractor pieces in a good chess problem.) >> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >>"Distractor pieces" went out of fashion about a century ago -- >>nowadays every piece and pawn in a good chess problem must have >>some specific function (i.e. the problem must become unsound or >>lose thematic content if any one or more pieces is/are deleted). >A whole century? Wasn't Sam Loyd composing chess puzzles into >the 1900's? Or was that, like Raymond Smullyan's retro puzzles, >"far behind what the REAL puzzle-makers were doing"?
Loyd's dates are 1841-1911 (according to both hollis.harvard.edu and http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Loyd.html; see also http://www.mathe.tu-freiberg.de/~hebisch/loyd.html). I'm not competent to write with authority on the 19th-century history of the chess problem, but Loyd is usually regarded as a pioneer on the road that developed into the modern problem art, and my impression is that he did most of his creative chess work in the first half of his life. Raymond Smullyan is a great popularizer of retrograde analysis, but he did not pioneer the art or advance its state.
--Noam D. Elkies (delete monster from e-address to reply)
Noam D. Elkies <elk...@mminotaurath.harvard.edu> writes:
>Loyd's dates are 1841-1911 (according to both hollis.harvard.edu and >http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Loyd.html; >see also http://www.mathe.tu-freiberg.de/~hebisch/loyd.html). >I'm not competent to write with authority on the 19th-century >history of the chess problem, but Loyd is usually regarded as >a pioneer on the road that developed into the modern problem art, >and my impression is that he did most of his creative chess work in >the first half of his life.
I just vaguely remember "The Steinitz Gambit" being composed by Loyd in 1905 ... come to think of it, that problem may not have any distractor pieces...
-- Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- C is for Cookies. Perl is even better for Cookies.
Wei-Hwa Huang <whu...@ugcs.caltech.edu> wrote: >Noam D. Elkies <elk...@mminotaurath.harvard.edu> writes: >>Loyd's dates are 1841-1911 (according to both hollis.harvard.edu and >>http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Loyd.html; >>see also http://www.mathe.tu-freiberg.de/~hebisch/loyd.html). >>I'm not competent to write with authority on the 19th-century >>history of the chess problem, but Loyd is usually regarded as >>a pioneer on the road that developed into the modern problem art, >>and my impression is that he did most of his creative chess work in >>the first half of his life. >I just vaguely remember "The Steinitz Gambit" being composed by Loyd in >1905 ... come to think of it, that problem may not have any >distractor pieces...
1903, according to http://www.knossos.gr/~strataki/stein1.html ; The diagram is crowded (it's not easy to realize such a theme), but I don't see any obviously superfluous pieces, let alone pieces whose only function is to distract the solver.
In any case, I don't see any reason why there shouldn't be distractors, especially given a case like the Minotaur Maze or chess puzzles. With these types of things, they're meant to make you think. If a chess puzzle was given with only necessary pieces, it would seem to me that it would be rather simple to find the solution. Personally, I prefer positions that have actually resulted during matches, instead of some thought-up puzzle with no "extra" pieces.
kIdMiGaRu <anarch...@rocketmail.com> writes: >In any case, I don't see any reason why there shouldn't be distractors, >especially given a case like the Minotaur Maze or chess puzzles. With >these types of things, they're meant to make you think.
Mostly because distractions are often irrelevant to the actual solution of the puzzle. We don't really care that the four members are members of U2 -- and after going through hundreds of puzzles, the extra information is just annoying. For the matter of a maze, the issue is more debatable -- a maze without any "distractions" would just be a straight path!
I think some distraction is okay, but it has to be elegant -- a maze with lots of really short dead-ends is just annoying, while a maze with a really large branch that keeps me fooled for hours is fine.
>If a chess >puzzle was given with only necessary pieces, it would seem to me that it >would be rather simple to find the solution.
Obviously you haven't seen any really hard chess puzzles!
>Personally, I prefer >positions that have actually resulted during matches, instead of some >thought-up puzzle with no "extra" pieces.
Therein lies the difference between chess puzzles and chess studies. Don't think of them as puzzles from a chess game; think of them as puzzles with abstract pieces that just happen to use a familiar ruleset. -- Wei-Hwa Huang, whu...@ugcs.caltech.edu, http://www.ugcs.caltech.edu/~whuang/ --------------------------------------------------------------------------- C is for Cookies. Perl is even better for Cookies.
