The New Sudoku Players' Forum

[Smythe Dakota]

Well, I finally finished your two January 28 puzzles. The 8x8 closed knight's tour took a while (an hour here, an hour there, over several days) because, I think, it took me some time to figure out the basic techniques. Maybe I'll be able to do your next one faster. The 8x8 closed wazir's tour was ridiculously easy (5 minutes or so), perhaps because I have been doing Marilyn's puzzles in Parade magazine (Numbrix) for at least a year or two.

I'm wondering if there are any lurkers following this thread. So far it's just Serg and dyitto (contributing some of the higher-level comments) and me (coming in at a lower level and working by hand). Keep it up! I haven't tried your post-January 28 concoctions just yet, but I glanced briefly at the 8x8 king's tour. In that one, a few concepts are obvious, but applying them still seems to lead to multiple paths.

Bill Smythe

[Smythe Dakota]

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

Closed King Tour 8x8

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

Code: Select all

.. .. .. .. 01 .. .. ..
.. 21 .. .. .. .. .. ..
33 .. .. .. .. .. 53 ..
.. 27 .. .. .. .. .. ..
.. .. .. .. .. .. .. 57
06 .. 10 .. .. .. .. ..
.. .. .. .. .. .. 59 ..
.. .. 08 .. .. .. .. 45

[tarek]

Indeed Bill ... The top Rt Corner is forced to be .......

In a similar fashion, you can stretch the longest path centering around a given glue that can't touch the desired target cell. That desired cell can't be any of the values along that path. If this is done for all clues then you'll see that only one possibility remains.

So for 1 the path is 63-3, for 21 it is 16-26, for 33 it is 27-39 & for the 10 it is 6-14

For this strategy the target cell should be as far as possible from most of the other solved cells to maximize the result.

[tarek]

8x8 Closed King's tour

Code: Select all

01 .. .. 04 24 .. .. 21
.. .. 61 .. .. 25 .. ..
.. 60 .. .. .. .. 47 ..
57 .. .. .. .. .. .. 49
30 .. .. .. .. .. .. 16
.. 37 .. .. .. .. 51 ..
.. .. 43 .. .. 52 .. ..
35 .. .. 42 53 .. .. 13

8x8 Closed King's tour

Code: Select all

01 .. .. 04 16 .. .. 49
.. 02 .. 15 05 .. 50 ..
.. .. 14 .. .. 51 .. ..
31 13 .. .. .. .. 52 46
12 30 .. .. .. .. 45 53
.. .. 29 .. .. 44 .. ..
.. 28 .. 24 40 .. 55 ..
27 .. .. 39 42 .. .. 57

The next next one should be tough requiring <=1 Guess

8x8 Closed King's tour

Code: Select all

.. .. .. .. 01 03 .. ..
.. 62 .. .. .. .. .. ..
36 .. .. .. .. .. .. 26
.. .. .. .. .. .. .. 27
.. .. .. .. .. .. .. ..
39 .. .. .. .. .. .. ..
.. .. .. .. .. .. 30 ..
54 .. .. 42 .. .. .. 13

The next is an open King's tour, so very close to Hidato

6x6 Open King's tour

Code: Select all

.. .. 01 12 .. ..
.. .. .. .. .. ..
35 .. .. .. .. 22
15 .. .. .. .. 08
.. .. .. .. .. ..
.. .. 28 29 .. ..

[tarek]

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!!!!]

Code: Select all

.. .. .. ..
.. .. .. ..
11 .. .. 12
.. 05 14 ..

Here are 3 Open Toroidal King's tour puzzles. The last puzzle is a toughie requiring 1 Lucky guess. Because the last 2 puzzles have the 1 & 64, you can think of them as Toroidal Hidato puzzles as well.

Code: Select all

16 .. .. 12 06 .. .. 21
.. 40 .. .. .. .. 33 ..
.. .. .. 09 59 .. .. ..
51 .. 24 .. .. 58 .. 38
27 .. 25 .. .. 36 .. 47
.. .. .. 62 03 .. .. ..
.. 44 .. .. .. .. 55 ..
15 .. .. 42 31 .. .. 19

Code: Select all

.. .. .. .. .. .. .. ..
.. .. .. .. 15 .. .. 27
.. .. .. .. 47 .. .. 60
.. .. 19 .. .. .. 31 39
51 .. .. 64 .. .. .. 52
01 .. 35 .. .. .. .. ..
55 .. 43 .. .. .. .. ..
.. .. 57 07 .. .. 11 ..

Code: Select all

.. .. .. .. .. .. .. ..
.. .. .. .. 01 .. .. ..
.. .. .. 37 21 10 .. ..
29 06 .. .. .. .. .. 04
13 .. 59 .. .. .. 33 ..
.. .. .. .. 64 .. .. ..
.. 46 .. .. .. .. .. 41
.. .. .. .. 24 .. .. ..

[tarek]

Code: Select all

.. 01 .. 09 ..
19 18 .. 05 13
.. .. .. .. ..
20 23 .. 06 12
.. 24 .. 04 ..

Code: Select all

.. 01 03 16 ..
10 .. .. .. 19
09 .. .. .. 18
25 .. .. .. 05
.. 12 13 14 ..

Code: Select all

.. 06 .. .. 12 ..
36 .. 04 01 .. 14
.. 34 .. .. 28 ..
.. 09 .. .. 10 ..
17 .. 23 30 .. 25
.. 19 .. .. 20 ..

[EDIT 01: Corrected broken links to images]

[tarek]

The next 5 puzzles are 8x8 Open Toroidal Wazir tour puzzles
The 1st 2 should be solvable.
The last 3 may need a single guess to solve.

[tarek]

I'm wondering if there are any lurkers following this thread. So far it's just Serg and dyitto (contributing some of the higher-level comments) and me (coming in at a lower level and working by hand). Keep it up!

Bill I hope you're well,

This is possibly silly & unrelated to the topic but I stumbled upon this page today

http://www.ajc.com/news/bill-smythe-former-tech-1355062.html

Your comments to what is in the link would remove some of the doubts

tarek

[Smythe Dakota]

.... Your comments to what is in the link would remove some of the doubts ....

Ooh. Thanks for pointing that out. As Mark Twain would have said, this report (if it were about me) would be greatly exaggerated.

I'm actually from Chicago, but I grew up in South Dakota. My moniker, shortened from the original "The Kid from Smythe Dakota", was given to me in Chicago by a humor-loving acquaintance who liked to pun people's names.

If you google me, you'll find several references to "Bill Smythe" and "William Smythe" that are not me -- as well as some that are. Mostly you'll find me on the U.S. Chess Federation discussion forums at http://www.uschess.org/forums/. That's a membership organization, but you can read (but not contribute to) the forums without being a member.

As for your puzzles, you're cranking them out faster than I have time to try to solve them. I do have a life (well, at least I like to think so) but sooner or later I still might get around to some of them.

Thanks for your concern!

Bill Smythe

[simon_blow_snow]

So far I've seen King, Queen, Rook, Knight, Wazir (which can arguably replace the Pawn) but haven't seen a good ol' Bishop yet. It is indeed possible if you play it on an odd-width toroidal board with obstacles (so the piece can move between black & white cells). Here is a very simple 3x3 example:

Code: Select all

3x3 Open Toroidal Bishop tour with obstacles puzzle

...
69.
.14

Solution: Show

Code: Select all

357
692
814

Feel free to create bigger (e.g. 5x5) puzzles with higher difficulty!

[Smythe Dakota]

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)

[tarek]

.... Your comments to what is in the link would remove some of the doubts ....

Ooh. Thanks for pointing that out. As Mark Twain would have said, this report (if it were about me) would be greatly exaggerated.

Well for what it's worth, you didn't strike me as a Recorder playing person as the late Smythe did

I had to be sure because it was only by mistake that your name ended on the google search bar and the news item was from the day before (a bizarre coincidence!)

[tarek]

So far I've seen King, Queen, Rook, Knight, Wazir (which can arguably replace the Pawn) but haven't seen a good ol' Bishop yet. It is indeed possible if you play it on an odd-width toroidal board with obstacles (so the piece can move between black & white cells).

A great idea Simon. It shouldn't need much extra programming I hope because I've already programmed the Queen version. Thanks for the example which will be helpful to test against.

Hopefully something by the weekend!!!

The next post will be an open knight's tour regular board puzzle that I've already prepared.

Tarek

[Smythe Dakota]

.... Well for what it's worth, you didn't strike me as a Recorder playing person as the late Smythe did ....

Nope, I just play my Frankie Yankovic CDs. (Also bang around on the piano a bit.)

Bill Smythe

[Serg]

Hi, Bill!
I am glad to see you OK. I really worried about you after tarek's post, because I thought you concern to mathematics or even you are mathematician. So, the news found by tarek seemed plausible.

Serg