Fairy chess piece tour puzzles including Numbrix & Hidato

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Re: Fairy chess piece tour puzzles including Numbrix

Postby tarek » Thu Jan 19, 2012 8:23 am

dyitto wrote:This solver does wazir and king.
The obstacle variant for rook and queen is an extension of the same program - on my laptop and still quick&dirty. :oops:
The hidato then is nothing more than a King's tour while Numbrix is nothing more than a Wazir's tour. Still very exciting logic puzzles. Great that there is a solver/generator available to download, the Wazir's tour (Numbrix) possibility is a bonus.

Funny how all of this came to my attention. A comment mentioning Numbrix by Bill on another thread!!!
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Re: Fairy chess piece tour puzzles including Numbrix

Postby tarek » Thu Jan 19, 2012 9:26 am

Smythe Dakota wrote:
tarek wrote: .... ooops :oops: , I haven't thought about [ square color ] ....

I worked around it by putting a blank piece of paper on top of the printout, and copying the givens to the blank page. Just enough of the diagram showed through the blank page to guide me as to where the borders lay.

I made the black squares now light gray with the Font being black.
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Closed 8x8 Knight Tour

Postby tarek » Thu Jan 19, 2012 11:40 pm

Here is the Closed Knight's tour puzzle I promised. Fully symmetric.

Image

Code: Select all
.. .. .. .. .. .. .. ..
.. .. .. 01 18 .. .. ..
.. .. 15 .. .. 64 .. ..
.. 29 .. .. .. .. 04 ..
.. 20 .. .. .. .. 33 ..
.. .. 22 .. .. 57 .. ..
.. .. .. 36 53 .. .. ..
.. .. .. .. .. .. .. ..
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Re: 8x8 Queen tour with obstacles

Postby tarek » Sun Jan 22, 2012 10:16 am

Here is my attempt at a 8x8 queen's tour with obstacles with the same rules as dyitto's puzzle here.

Squares Numbered 1 .. 64 All should be visited during tour.
Queen moves between successive numbered squares
Each visited square forms an obstacle to Queen's movement

Image

Code: Select all
06 15 14 .. .. 19 20 07
23 .. .. 26 22 .. .. 28
13 .. .. .. .. .. .. 64
.. 35 .. 01 32 .. 21 ..
.. 37 .. 41 10 .. 61 ..
43 .. .. .. .. .. .. 60
39 .. .. 55 12 .. .. 58
33 45 52 .. .. 49 47 09
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Re: 8x8 Rook tour with obstacles

Postby tarek » Sun Jan 22, 2012 10:19 am

Here is my attempt at a 8x8 Rook's tour with obstacles.

Squares Numbered 1 .. 64 All should be visited during tour.
Rook moves between successive numbered squares
Each visited square forms an obstacle to Rook's future movement

Image

Code: Select all
06 .. 13 .. .. 16 .. 07
.. .. 21 .. .. 24 .. ..
29 30 .. .. .. .. 35 28
.. .. .. 01 02 .. .. ..
.. .. .. 04 03 .. .. ..
44 45 .. .. .. .. 55 47
.. .. 49 .. .. 61 .. ..
10 .. 37 .. .. 60 .. 09
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Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Postby Serg » Sun Jan 22, 2012 2:19 pm

Hi, tarek!
Thank you very much for this thread! I tried "King's tour" - it is nice puzzle with great possibilities for player's analisys. It is more interesting even than sudoku in some aspects. Separate Universe being not so carefully discovered as sudoku.

It turns out that "King's tour" is a kind of Hidato puzzle (thanks to dyitto for his clarification) with minor differences. Wikipedia says: "Hidato is a logic puzzle game invented by Dr. Gyora Benedek, an Israeli mathematician". But when was it invented? I assume Hidato was invented in 2008, is it so? Maybe dyitto has more accurate information about it?

Sudoku and Hidato have many common properties, and at least some sudoku solving methods can be used for Hidato solving (for example, naked and hidded pairs, trios, etc.). Hidato has even its own unavoidable sets. Maybe it is not so curious, because both puzzles are kinds of number permutation puzzles with constraints.

I wrote a solver to verify King's tour puzzles posted by youself. When I coded my solver ("smart" backtracking solver, it finds naked and hidded singles, otherwise - backtracks (T & E)), I discovered that "candidate finding" phase for King's tour is not trivial and is more complicated than for sudoku. It seems to me "Pencilmark style" manual solving of King's tour is possible but not feasible (at least, for hard puzzles), because the same cell can be occupied by huge number of candidates (up to 64 per cell).

tarek wrote:These 8x8 (Chess board) puzzles have been verified to be minimal and to have a unique solution by my solver, I couldn't find an independent solver to verify this. :(

here is a sample open King's tour puzzle & solution
Code: Select all
22 21 00 00 27 00 63 00
00 00 00 01 00 00 00 00
38 00 00 00 00 00 00 00
00 00 00 11 00 00 00 00
49 00 00 00 00 00 00 00
00 00 00 00 00 13 58 00
45 00 00 00 00 33 00 00
00 00 00 00 00 00 00 00

22 21 25 26 27 03 63 64
23 24 20 01 02 28 04 62
38 09 10 19 18 05 29 61
39 37 08 11 06 17 30 60
49 40 36 07 12 31 16 59
48 50 41 35 32 13 58 15
45 47 51 42 34 33 14 57
46 44 43 52 53 54 55 56


I confirm that this puzzle has unique solution. My solver solved it in 0.02 sec. But it is not minimal. You can delete moves 21, 22 and 58 (only one move can be deleted at once), and the puzzle will still have unique solution. (But no additional move removals are possible.)

Then I tried to solve other posted King's tour puzzles. All puzzle, except Puzzle 6, have unique solutions. Here is strange Puzzle 6, containing 9 rows and duplicated moves ("01" and "64").
tarek wrote:
Code: Select all
60 61 19 63 64 01 35 34
00 18 09 10 00 00 13 28
00 00 00 00 11 12 00 00
00 00 00 00 00 00 01 00
00 00 00 00 00 00 00 49
00 00 00 00 00 00 00 00
00 00 00 44 04 51 00 00
00 00 00 00 00 00 00 00
64 00 00 42 00 00 00 00


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Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Postby tarek » Sun Jan 22, 2012 2:43 pm

Thanks Serg,

The Hidato is a King's tour while Numbrix is a Wazi'rs tour (which you can modify your solver easily to accommodate it)

The grid is a big sector where the clue can occur once. Therefore you could look for sets of sizes up to ( grid size - solved squares)

I will correct that grid which at 1st glance has an extra row, thanks
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Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Postby Serg » Sun Jan 22, 2012 8:59 pm

Hi, tarek!
tarek wrote:The Hidato is a King's tour while Numbrix is a Wazi'rs tour (which you can modify your solver easily to accommodate it)

The Hidato has a limitation comparing to King's tour. Hidato claims the first and the last moves must be among puzzle's clues. So, you cannot use Hidato solver to solve King's tour puzzles, not containing "01" or "64" clues in the initial configuration.

If we consider simplest Wazir's tour variant (not closed, playing on plain board), it is equivalent to Numbrix puzzles. But, I think, Numbrix solver cannot solve closed Wazir's tour and/or Wazir's tour on toroidal board.

You published so many flavours of puzzles! For what kinds of them do you really need independent confirmation?

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Re: Fairy chess piece tour puzzles including Numbrix & Hidat

Postby tarek » Mon Jan 23, 2012 9:26 am

Serg wrote:You published so many flavours of puzzles! For what kinds of them do you really need independent confirmation?

I think I'm quite happy with the puzzles now ... Unless there are reports otherwise, all published puzzles should have a unique single solution.

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Closed Wazir tour 8x8

Postby tarek » Mon Jan 23, 2012 11:49 pm

This should be a difficult close Wazir tour.

Wazir: Orthogonal 1 square moves
Tour: Each square of the 8x8 chess board is visited once
Closed: Last visited square is one move away from the First.

Image

Code: Select all
.. .. .. .. .. .. .. ..
.. .. 01 .. .. 08 .. ..
.. 59 .. .. .. .. 12 ..
.. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. ..
.. 42 .. .. .. .. 23 ..
.. .. 50 .. .. 25 .. ..
.. .. .. .. .. .. .. ..
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Re: 4x4 Rook Tour with obstacles

Postby tarek » Wed Jan 25, 2012 12:54 am

This 4x4 Rook Tour with obstacles should have a single solution. Although having few clues, the small grid size should limit the difficulty.

Image

Code: Select all
.. .. .. ..
.. .. 01 ..
.. 06 .. ..
.. .. .. 16
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Re: 4x4 Rook Tour with obstacles

Postby Smythe Dakota » Thu Jan 26, 2012 3:30 pm

tarek wrote:This 4x4 Rook Tour with obstacles should have a single solution. Although having few clues, the small grid size should limit the difficulty. ....

I agree it seems to have a single solution. But I find these puzzles a bit tedious, involving a lot of T&E. Even in this little 4x4 one, there were two candidate locations for the 15, each of which led to two for the 14. Each of the resulting four paths then continued without further branching until they got down to about the 8. At that point, three of them ran into a dead end, and the fourth was the solution.

With so much T&E, I am losing my inclination to try many more of these. The 8x8 closed knight's tour, for example, seems to yield only about 6 answers before it branches out wildly. I might take another crack at that one some day, but only If I have lots of spare time.

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Re: Regarding difficulty

Postby tarek » Thu Jan 26, 2012 5:22 pm

Smythe Dakota wrote:But I find these puzzles a bit tedious, involving a lot of T&E.

Thanks for taking interest in them ...

My feeling is that the puzzles posted are not suitable for manual solving because of this ... I'm sure that with a better puzzle selection these variants can be enjoyable ...

The 3 clue puzzle is the least number of clues to have in a diagonal symmetry puzzle without having multiple solutions, that probably has reflected on the difficulty.

In the solver, I'm using a 1 step LookAhead before guessing. If I increase that to 4 for The Wazir & 2-3 for the Knight then that might give an indication of difficulty ... For the King's tour A Lookahead of 3 can cover 49 squares. The Rook & Queen Tours are going to be tedious beyond 1 because a LookAhead of 2 can cover all squares on any rectangular chess board.
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Re: Human Solvable puzzles

Postby tarek » Sat Jan 28, 2012 12:21 pm

These puzzles should be solvable ... I've been testing a method which is quick but it may over-estimate the puzzle's difficulty

Closed Wazir Tour 8x8

Image

Code: Select all
.. .. 01 .. .. 04 .. ..
.. 61 .. .. .. .. 06 ..
53 .. .. .. .. .. .. 10
.. .. .. 33 32 .. .. ..
.. .. .. 24 25 .. .. ..
48 .. .. .. .. .. .. 13
.. 46 .. .. .. .. 15 ..
.. .. 42 .. .. 19 .. ..


Closed Knight Tour 8x8

Image

Code: Select all
.. .. 01 .. .. 16 .. ..
.. .. 32 .. .. 37 .. ..
53 34 .. 64 47 .. 39 28
.. .. 18 .. .. 61 .. ..
.. .. 35 .. .. 40 .. ..
04 19 .. 57 10 .. 42 45
.. .. 21 .. .. 44 .. ..
.. .. 56 .. .. 11 .. ..


The last puzzle should not require any guessing if you can see 3 moves ahead.

tarek
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Re: Solvable close King & Wazir puzzles

Postby tarek » Sun Jan 29, 2012 4:53 pm

The following 2 puzzles should be solvable

Closed Wazir Tour 8x8 05

Image

Code: Select all
.. .. .. .. .. .. .. 01
.. .. .. .. .. .. .. ..
.. .. .. .. 06 .. .. ..
.. .. .. .. .. 16 .. ..
.. .. 26 .. .. .. .. ..
.. .. .. 40 .. .. .. ..
.. .. .. .. .. .. .. ..
51 .. .. .. .. .. .. ..


Closed Wazir Tour 8x8 06

Image

Code: Select all
01 .. .. .. .. .. .. 08
.. 33 .. .. .. .. 12 ..
.. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. ..
.. 42 .. .. .. .. 23 ..
54 .. .. .. .. .. .. 21


The following probably needs one guess if you can see 7 moves ahead & 2 if you can see 6
(This method most likely over-rates puzzles, you may find these easier than proposed!)

Closed Wazir Tour 8x8 07

Image

Code: Select all
.. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. 01
.. .. 07 .. .. .. .. ..
.. .. .. .. .. .. .. ..
.. .. .. .. 47 .. 33 ..
.. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. ..


& Finally This one which should be easy if you can see 6 moves ahead

Closed King Tour 8x8

Image

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