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Solving wapati's grids by guessing
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Frank

Joined: 24 Jan 2008
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PostPosted: Thu Jan 24, 2008 9:28 pm    Post subject: Solving wapati's grids by guessing Reply with quote

Hallo to everybody,
probably I cannot participate to this forum because I'm a T&E sudoku solver.
Nevertheless, confrontation of different ways on solving wapati's truly interesting grids could be useful and suitable for some discussions.
So, I ask the Site Administrator the authorization to enter in this forum.
Thanks
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Ruud
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PostPosted: Fri Jan 25, 2008 1:03 am    Post subject: Reply with quote

we're very open-minded here. go ahead. Smile

Ruud
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Frank

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PostPosted: Thu Jan 31, 2008 10:51 am    Post subject: Reply with quote

...

Last edited by Frank on Tue Feb 12, 2008 8:33 am; edited 1 time in total
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Frank

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PostPosted: Thu Jan 31, 2008 11:06 am    Post subject: Reply with quote

As a matter of principle, any sudoku puzzle is solved following the method suitable to the solver. Any way is good to reach the target! But inside a specific zone, the choice of the solution method is commonly seen as unclever or unelegant.
I'm referring to grids, like wapati's, which cover the zone from puzzles solved by logic to the ones solved by guessing (T&E).
In this forum are shown a lot of techniques to overcome, whereit's possible, the T&R solution, assimilated perhaps to a sort of brute force applied by hand, not via computer program, I mean.
Sometimes, and wapati's puzzles are a good field of investigation, the solution can be reached after few trials, appropriately chosen, of course!
For example, we examine now the following grid:

Quote:

Posted: Mon Jan 21, 2008 3:14 pm
Ruud wrote:
so much fun with only 4 digits Very Happy
An unusual puzzle it was.
This one is lots of small patterns.


Code:

7 3 .|4 . 8|5 6 .
9 6 .|. . .|7 . .
. . .|. . 3|. 9 .
-----+-----+-----
6 . .|. . .|. 5 .
. . .|. . 7|6 . .
5 . 4|. 1 .|. . 9
-----+-----+-----
3 5 .|. 4 .|. . .
8 . 6|7 . .|. . .
. . .|. . 1|. . 5
#
#      Note: rows are marked A..I, columns 1..9.
#
# (Node 1)  2I1 (alias E1)  (no marks)
#            |
# (Node 2)   +--- 5H5 (alias 9I2) (marked^)
#                 |
# (Node 3)        +--- 9H2 (alias 9I2) (marked~)  [contradiction]
#                 +--- 9I2 (marked o)  solves the puzzle
#


My hand-solution can be seen here:
-------------
Note: unfortunately I haven't 5 posts to be authorized for HTM links.
I cancel it, but the grid misses in clarity. Stange matter but it's
the forum rule!
-------------------
and below I describe some details of the procedure.
So, probably other readers of this forum can see different ways, by using less than 3 nodes.
It could be an optimum subject of discussion.


Last edited by Frank on Tue Feb 12, 2008 8:47 am; edited 1 time in total
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Frank

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PostPosted: Thu Jan 31, 2008 11:18 am    Post subject: Reply with quote

...

Last edited by Frank on Tue Feb 12, 2008 8:49 am; edited 1 time in total
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Frank

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PostPosted: Thu Jan 31, 2008 11:44 am    Post subject: Reply with quote

...

Last edited by Frank on Tue Feb 12, 2008 8:48 am; edited 1 time in total
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Frank

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PostPosted: Thu Jan 31, 2008 11:49 am    Post subject: Reply with quote

Post n.3 repeated! This should be my post n.6.

Code:

7 3 .|4 . 8|5 6 .
9 6 .|. . .|7 . .
. . .|. . 3|. 9 .
-----+-----+-----
6 . .|. . .|. 5 .
. . .|. . 7|6 . .
5 . 4|. 1 .|. . 9
-----+-----+-----
3 5 .|. 4 .|. . .
8 . 6|7 . .|. . .
. . .|. . 1|. . 5
#
#
# (Node 1)  2I1 (alias E1)  (no marks)
#            |
# (Node 2)   +--- 5H5 (alias 9I2) (marked^)
#                 |
# (Node 3)        +--- 9H2 (alias 9I2) (marked~)  [contradiction]
#                 +--- 9I2 (marked o)  solves the puzzle



My hand-solution can be seen here:
http://img31.picoodle.com/img/img31/4/1/27/f_wap21janm_636d9ed.jpg
and below I describe some details of the procedure.


Last edited by Frank on Tue Feb 12, 2008 9:02 am; edited 1 time in total
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Frank

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PostPosted: Thu Jan 31, 2008 4:32 pm    Post subject: Reply with quote

Now everything is normalized, I've no troubles to enter my posts, I mean.
So, my next proposal is wapati's grid of Jan.29,2008, that is the following one:

Code:

. 9 .|. 5 .|3 . .
8 . 2|. . .|. . 9
. 6 .|. . 2|. . 1
-----+-----+-----
. . .|5 . 1|. . 4
3 . .|. . .|7 . .
. . 8|7 . .|. . .
-----+-----+-----
2 . .|. 1 .|. 4 8
. . .|. . .|2 . 3
. 4 6|8 . .|1 5 .

My solution can be seen here:
http://img26.picoodle.com/img/img26/4/1/31/f_wapjan29m_287de60.jpg

Comments: in such a case they arrive to the target by using only one node:

Node 1 3B2 (alias 3G2)
which solves the puzzle
-----


Last edited by Frank on Tue Feb 12, 2008 9:04 am; edited 1 time in total
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Frank

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PostPosted: Thu Jan 31, 2008 5:57 pm    Post subject: Reply with quote

...

Last edited by Frank on Tue Feb 12, 2008 8:50 am; edited 1 time in total
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Frank

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PostPosted: Fri Feb 01, 2008 8:50 am    Post subject: Reply with quote

This is the puzzle published by wapati a couple of days ago in his forum section.
See the URL below for my solution, carried out by using pencil&rubber, as usual. Some remarks to describe the symbols: cells marked with left-top corner come from logic solution, while the ones (only one in this grid) circled are referred to a double trial: if in the tree the initial tentative fails, so the second is definitive and other cells (unmarked) are filled consequently.

http://img30.picoodle.com/img/img30/4/2/1/f_wap30janm_bb1dde2.jpg

Code:

# wapati's grid of Jan.30,2008
#
1 . .|3 . .|. 2 4
. . .|9 . .|6 5 .
. . .|. 2 .|. . 7
-----+-----+-----
6 3 .|. . 5|8 . .
. . 5|. . .|. 3 .
. . .|8 . 6|. . .
-----+-----+-----
. 2 .|1 . .|. 9 .
5 8 .|. 4 .|2 . .
7 . 9|. . .|. . .
#
# ----- 1st Tree -----
#  1) 9F1 (alias 9C1) [contradiction]
#     9C1 Definitive (9 in C1, circled)
#
# ----- 2nd Tree -----
#  2) 7E7 (alias 7G7)
#      |
#      +-- 3C7 (alias 3G7) (mark ^)
#          which gets the target
#

And now, I'm waiting for some readers' comments.
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wapati

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PostPosted: Sat Feb 02, 2008 6:06 pm    Post subject: Reply with quote

I agree that everyone should use the methods that they prefer.

I don't expect that many people prefer to guess.

I have read that it is the fastest method, when you guess correctly. Smile
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Frank

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PostPosted: Sat Feb 02, 2008 7:24 pm    Post subject: Reply with quote

wapati wrote:
I agree that everyone should use the methods that they prefer.

I don't expect that many people prefer to guess.

I have read that it is the fastest method, when you guess correctly. Smile


Thanks for your answer, wapati. You are right when you say that the guess should be chosen appropriately, otherwise any tentative is randomized.
I've appreciated your grids because they ever admit the double trial (on/off, I mean) and don't exceed 3 trees.
With my HTM links I want to spread my hand-solver experience to the forum readers and meantime enjoy myself. Never mind if readers are many or few.
Thanks again.
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Frank

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PostPosted: Sun Feb 03, 2008 1:39 pm    Post subject: Reply with quote

An empiric way to choose the initial on/off cell is to select it from a column of different blocks, namely 5 and 8 in the grid of the following link

http://img26.picoodle.com/img/img26/4/2/3/f_wap01febm_64b1a4c.jpg

Code:

# wapati's grid of Feb.1,2008
#
. 1 .|. . .|5 . 7
5 . .|. . 8|. 9 .
. . .|5 4 .|1 . .
-----+-----+-----
. . 3|. . 2|8 . 9
. . 4|. . .|. . 2
. 9 .|8 . .|3 5 .
-----+-----+-----
7 . 5|3 . 9|2 . .
. 2 .|. . 5|. . .
3 . .|2 6 .|. . .
#
# ----- 1st tree ------
#    4F6 (alias 4I6)
#    which solves the puzzle
#
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Frank

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PostPosted: Mon Feb 04, 2008 5:23 pm    Post subject: Reply with quote

Now I want to present a typical example of a grid where the human mind prevails on brute force.
Most sudoku solvers commonly think, erroneously from my point of view, that guessing is synomym (equal) to brute force. The mind of man is tremendously slower than a computer machine but surely clever.
In this wapati's grid
http://img02.picoodle.com/img/img02/4/2/4/f_wap02febm_9be8f67.jpg
the first tentative (6 in E1) has been quickly abandoned because the procedure didn't free further cells; next choice (7 in G4) as first tree goes to the target throughout two more bifurcations.

Code:

#
# wapati's grid of Feb.02,2008
#
. . 4|. . 1|. 7 .
. . 8|6 . 7|. . 3
7 5 .|. . .|8 . .
-----+-----+-----
. 8 .|. 9 6|. 1 .
. . .|5 . .|. . .
9 3 .|1 . .|. . .
-----+-----+-----
. . 6|. . .|. . 2
5 . .|8 . .|. . .
. 7 .|. . .|5 . 8
#
#   ----- 1st Tree -----
#   1) 6E1 (alias 6A1) [out, as said above]
#
#   ----- 1st Tree -----
#   1) 3D4 (alias 3D7) [contradiction]
#      3D7 (definitive) [3 in D7 circled]
#   ----- 2nd Tree -----
#   2) 7G4 (alias 7D4)
#      |
#      +-- 6E2 (alias 6A2) [contradiction]
#      +-- 6A2 (mark o)
#          |
#          +-- 3I1 (alias 3A1)
#              which solves the puzzle
#
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Frank

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PostPosted: Tue Feb 05, 2008 11:29 am    Post subject: Reply with quote

....

Last edited by Frank on Tue Feb 12, 2008 8:30 am; edited 2 times in total
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