Fairy chess piece tour puzzles including Numbrix & Hidato

For fans of all other kinds of logic puzzles

Solvable regular 8x8 Open Knight tour puzzles

Postby tarek » Wed Feb 22, 2012 7:41 pm

Regular 8x8 Open Knight tour puzzle 01
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Regular 8x8 Open Knight tour puzzle 02
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Regular 8x8 Open Knight tour puzzle 03
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Regular 8x8 Open Knight tour puzzle 04
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Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Postby simon_blow_snow » Thu Feb 23, 2012 12:36 am

Smythe Dakota wrote:Thank you, simon_blow_snow, for your concern (which you edited out, within seconds, after I made my post -- I'm sure I was the only one who saw it!).

I have often wondered what it would be like to sneak back to life briefly, just long enough to attend one's own funeral as an invisible ghost, to see what people are saying about you. Alternatively, one could start a phony thread, on a forum like this, announcing one's own demise, and watch the reactions pour in.

Better yet, one could just wait for someone else to discover something, then wait a while before setting the record straight. I might have had a little more fun, had I waited a while!

:)

Bill Smythe (alive and kicking, as of 2-21-2012)

Haha, you can imagine my shock when I saw your emerging post just after finished clicking "submit". Luckily I wasn't talking anything bad about you. :lol:

Have to say the nice gentleman in that particular article in a certain way matched the public image you have been establishing here.
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Re: 4x4 ORR obstacles & 8x8 OKT

Postby simon_blow_snow » Thu Feb 23, 2012 1:21 am

tarek wrote:Here is a difficult 4x4 Rook tour with obstacles requiring 3 lucky guesses
[Edit: apologies for posting the wrong puzzle. This Rook tour puzzle is actually very difficult and Solvable!!!!]

Image

Code: Select all
.. .. .. ..
.. .. .. ..
11 .. .. 12
.. 05 14 ..

For some reasons I find these Rook puzzles with a small board the most appealing. Perhaps the "obstacles" property adds some exotic feel to them. So look forward to a good "Bishop with obstacles" puzzle. ;-)

Here is a brief walkthrough to this "very difficult and solvable" puzzle:

Hidden Text: Show
Firstly, the [13] must be in R3C3 or R4C4.
It cannot be in R3C3 as it would force R4C4=[15] and nowhere to go for [16].
Therefore R4C4 = [13].
Now the cells between [11] and [12] (R3C23) must be larger than them, only possibility: [16,15].

Code: Select all
.. .. .. ..
.. .. .. ..
11 16 15 12
.. 05 14 13

[04] & [06] must be in two cells out of R12C2+R4C1 to connect to [05].
So aside from [01,02,03], R12C34 must contain at least one of [07,08,09,10], call it [A].
R12C2 cannot be [04,06], or they will block the path from [11] to [A].
Thus R4C1 must be [04] or [06].
Hence R1C1 must be [03] or [07], R2C12 must be [10,09], R1C2 must be [06] or [04].
But R1C12 cannot be [07,04] blocking the path from [07] to [08].
Therefore R14C1 = [03,04], R1C2 = [06]

Code: Select all
03 06 .. ..
10 09 .. ..
11 16 15 12
04 05 14 13

To lead from [09] to [06], R12C3 = [07,08].
And finally R12C4 = [02,01].

Code: Select all
03 06 07 02
10 09 08 01
11 16 15 12
04 05 14 13
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Re: Solvable close King & Wazir puzzles

Postby Serg » Thu Feb 23, 2012 5:00 pm

Hi, all!

Smythe Dakota wrote:
tarek wrote: .... & Finally This one which should be easy if you can see 6 moves ahead

Closed King Tour 8x8

Image

After wasting a few hours over several days, I finally figured out the trick to solving this one. Since nobody else has posted yet, I assume nobody will object if I divulge the clue I finally figured out.

Just go to various obscure cells (corners, near-corners, etc) and ask yourself "what can go here?" -- "this cell must lie on the path from what to what?". Fill in the "what's" with various givens.

For example, can the upper right corner cell be on the path from 1 to 6? Nope.
From 6 to 8? Nope. From 8 to 10? Nope. From 10 to 21? Well, maybe.
From 21 to 27? Nope. From 27 to 33? Nope. From 33 to 45? Nope.
From 45 to 53? Nope. From 53 to 59? Nope. From 59 to 1? Nope.

The only possibility is from 10 to 21. This path can barely be stretched long enough, so immediately the value in the upper right cell is forced, along with five others, and four more are severely limited.

Once I figured out that trick, the complete solution took only about 15 more minutes.

Bill Smythe

tarek wrote:
Code: Select all
.. .. .. .. 01 .. .. ..
.. 21 .. .. .. .. .. ..
33 .. .. .. .. .. 53 ..
.. 27 .. .. .. .. .. ..
.. .. .. .. .. .. .. 57
06 .. 10 .. .. .. .. ..
.. .. .. .. .. .. 59 ..
.. .. 08 .. .. .. .. 45

Nice puzzle! I manually solved it. Even knowning Bill's hint (path from move 10 to move 21 must come through upper right corner) I spent an hour or more to solve it.
Then I checked this puzzle by my solver. This puzzle has unique solution. It is necessarily closed, since it will have non-unique solutions if we would treat it as open tour puzzle. (The concept resembling minimality of sudoku puzzles.)

It turns out, this puzzle is not minimal, because it still has unique solution after move "1" removal. (No other moves can be removed provided the puzzle must have unique solution.) I think human cannot solve this puzzle after move "1" removal.

tarek, thank you for your puzzles!

Serg
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Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Postby Smythe Dakota » Thu Feb 23, 2012 10:18 pm

simon_blow_snow wrote: .... Haha, you can imagine my shock when I saw your emerging post just after finished clicking "submit". Luckily I wasn't talking anything bad about you. :lol: ....

That's why sneaking back to life to visit one's funeral would be so enlightening. What people say about you after you're gone would almost certainly be different from some of the things they said before. :|

.... Have to say the nice gentleman in that particular article in a certain way matched the public image you have been establishing here.

I was thinking that, too. We're both math semi-geeks, in various strange ways. And we're both somewhat musical -- again, in strange ways.

Bill Smythe
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Re: Solvable close King & Wazir puzzles

Postby Smythe Dakota » Thu Feb 23, 2012 10:23 pm

Serg wrote: .... It turns out, this puzzle is not minimal, because it still has unique solution after move "1" removal. (No other moves can be removed provided the puzzle must have unique solution.) ....

I think Tarek feels a moral obligation to always explicitly include 1 as a given in his closed tours -- along with a high number, in this case 59, which requires a maximally efficient path to the 1 (i.e. no horizontal backtracking or vertical backtracking between the two). This helps drive home the point that it is a closed tour.

Bill Smythe
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Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Postby simon_blow_snow » Sun Mar 04, 2012 4:52 am

It's been a while since the last update.

Just wondering how tarek has been going about creating that 5x5 (or higher) bishop's toroidal tour puzzle?
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Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Postby tarek » Sun Mar 04, 2012 8:20 am

I was very busy lately,

I attempted the bishop & found it needs some work because a square cane be attacked from 2 directions (The same can be said about toroidal Rook & Toroidal Queen on even length boards). A queen on an odd length board can attack a cell from 4 directions.

So in short, I know what I need to do but couldn't find the time :oops:

Hopefully I'll find some time within the next 2 weeks because I will be most likely very busy after that to dedicate any time towards creating puzzles until May :(

tarek
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