## Queen's tour hidato variant

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Queen's tour hidato variant

Suppose we place the queen on an empty chessboard. She should move according to the rules of chess and visit each square exactly once.

As additional constraint I'd like to pose that she is not allowed to pass squares that she has already visited.

(For example: she could move from e2 to e3, but then as next move e3-e1 is not allowed, since that would imply passing e2 and e2 has already been visited.)

The following grid describes such a path:

Code: Select all
`14;15;16;53;54;05;06;0713;38;39;55;52;09;10;0837;12;18;51;56;42;43;3024;49;50;45;58;57;41;2301;25;48;11;44;59;60;2226;47;17;36;31;61;40;2146;34;35;33;32;04;62;6427;28;29;02;03;20;63;19`

(1 is where the queen starts, 64 is where she ends, and no pair of consecutive numbers is separated by a lower number.)

The following puzzle is based on this constraint:

Code: Select all
`..;34;05;..;13;26;07;03..;33;..;..;..;08;..;0110;36;14;28;..;17;..;4630;..;..;38;..;57;..;51..;..;23;22;..;..;60;52..;42;43;..;..;64;..;58..;18;41;45;..;63;..;..16;40;..;..;20;55;..;48`

The remaining numbers must be completed.

www.scrybqj.com/scrybqjdocuments/queenstourpuzzle.pdf

Actually this is a Hidato variant.
Last edited by dyitto on Sat Aug 11, 2012 11:48 pm, edited 2 times in total.
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Queen's tour hidato variant

Using relatively simple moves, I reached this position with 9 cells left:

Then I could not make any progress without using "trial-and-error" approaches:

If R5C2=[25], then R45C2+R56C1={11,12,24,25} (naked quad), then R3C5+R7C1=[6,9], a contradiction because there is a [6] between the [8] and [9]. Therefore R5C2<>[25], =[29].

OR

If R3C5+R7C1=[12,11], then R4C2+R56C1 only have 2 candidates left ({24,25}), a contradiction. Therefore R3C5<>[12], =[6].

Is there a better step to advance from this position? It would be quite disappointing if this very nice puzzle could not be solved without "trial-and-error", especially this late in the solving path (all my steps before this were "trial-and-error" free).

If you generated this puzzle using a solver program, could you check out your program's step from this position please?

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Queen's tour hidato variant

I just realised a much better step:

If R3C5=[6], then R7C1<>[9] ([6] can't stand between [8] and [9]).
If R3C5=[12], then R7C1=[11], <>[9].
Therefore R7C1<>[9].

This seems much better than the trial-and-error approaches above, but can still be considered as a "bifurication chain" (albeit a pretty short one). I don't recall making any step with this "complexity level" before this position (but it's a pretty long solving path so I could have overlooked).

I'd still like a simpler and more "elegant" step.

simon_blow_snow

Posts: 85
Joined: 26 December 2010

### Re: Queen's tour hidato variant

Square c7: 31 is not allowed between 32 and 33
evert on the crashed forum

dyitto

Posts: 118
Joined: 22 May 2010
Location: Amsterdam

### Re: Queen's tour hidato variant

dyitto wrote:Square c7: 31 is not allowed between 32 and 33

Can't believe how I missed such an obvious elimination?!

So this puzzle can be solved with "elegant logic" after all! Many thanks for creating such an excellent challenge!

simon_blow_snow

Posts: 85
Joined: 26 December 2010