Peg Solitaire
1.99 Help file
Latest revision: May, 28th, 1999.
Contents:
Some Internet sites about Peg Solitaire 1.99 :
What is all about ?
Computer minimal requirements
To correctly run Peg Solitaire 1.99, you must have at less :
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Windows 95, 98 or NT installed on your computer. (No waranty for Win32s).
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24 Mb of RAM, to fully use the search engine capabilities.
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a 65536 colours (16 bits) video driver.
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French Solitaire
This board has 37 holes. Historically, it is one of the first to appear
in print. A particular feature is that the centre " single vacancy " problem
has no solution. (cf. De Bruijn's criterion, numbers n
& m). This board has 8 symmetries.
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English Solitaire
This board has 33 holes. Historically, despite of his name, it was
played above all in Germany. It has several features of interest. For instance,
you can resolve all " single vacancy - single survivor " complement problems.
This board has 8 symmetries.
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Square Solitaires
These boards have respectively 36 and 49 holes. 6x6 board received
more attention than the other. All complement problems are possible on
this latter. These boards have 8 symmetries.
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Wiegleb's Solitaire
This board has 45 holes. It first appears in print 1779. This board
didn't receive many attention. I managed to find a " 16 pegs long" sweep
using the Peg solitaire 1.99 search engine, what stands for a great accomplishment.
(cf. saved problems files). This board has 8 symmetries.
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Continental Solitaire
This board has 41 holes. Also called Hermary's board. Only two
" single - vacancy " problems are possible. (considering symmetries). A
specific criterion is used to prove the impossibility of some " single
vacancy - single survivor " problems. This criterion is represented by
the number "e", which is also called draught board
criterion. This board has 8 symmetries.
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Triangular Solitaires
These boards have respectively 15, 28 and 45 holes. They have been
studied by Martin Gardner in " Scientific American " columns. Triangular
solitaires are quite easy to resolve. The rules are the same as classical
boards, except that a peg can own a maximum of 6 neighbours instead of
4. These boards have 6 symmetries.
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Hexagonal Solitaires
These boards follow the same rules as Triangular Solitaires. They have
12 symmetries.
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Stellar Solitaire
This board follows the same rules as Triangular Solitaires. This board
has 12 symmetries.
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Lam Turki Solitaire
This board has 19 holes. Also called Solomon's board. Quite easy to
solve. This board has 12 symmetries.
Creating a problem
Designing the source board
You use the right button of your mouse to set or unset pegs on the
board. Note that you can rotate, mirror or inverse the board you are designing.
What is your target ?
A single peg on the board
If your objective is to reach a board with only one single peg at the
end (this is the most classic problem), then you must manage as below :
Firstly, start the " Options " dialogue box by selecting the " Board+Options
" command in the menu or by pressing [F5]. Secondly, select the " Target
Board " tab sheet (second tab sheet from the left) and then select the
" Single Peg " radio button. Now, you can close the dialogue box and you
can start solving the problem ...
A specific pattern
If your purpose is to reach a particular pattern, then you must manage
as below :
Firstly, start the " Options " dialogue box by selecting the " Board+Options
" command in the menu or by pressing [F5].
Secondly select the " Target Board " tab sheet (second tab sheet from
the left) and then select the " A specific pattern " radio button. Now
you can design the target board by clicking on the yellow bubbles. When
a peg is set then the bubble turns to blue. If you click once again on
a set peg, then it turns to red. In that case, the peg is said to be "marked".
It means that it must neither move nor be captured during the course of
play. There are famous problems that take in count this particular feature.
Have a look at the different numbers at the right of the dialogue box.
They can help you. (see the concerned items in the help index). You can
also use the six speed buttons (" (c) ", " C ", " R ", " I ", " F ", "
V "). They are useful to fill, clear, inverse, rotate, reflect the target
board currently being designed, or to set the complement problem of the
source board. Now, you can close the dialogue box and you can start solving
the problem ...
Solving a problem
How to manage to solve a problem ?
If you are not good enough or haven't got enough time to resolve the
problem by yourself, the computer can help. Once you have set the source
board and chosen your goal (just a single peg or a particular pattern),
you can start the search as explained below. After calculating, if your
computer tells you that it has found no solution because " depth parameter
" wasn't big enough, you must increase this value. Once you feel that your
computer resources are not performing enough (when your disk start swapping
...), then you can set the " Backtracking mode ". Cf. below (text in bold).
How to start the search ?
Click on the " Solve ! " item of the main menu. Now, your computer
is looking for a solution. You can also press the short cut key [F12] or
[Alt+S]. To halt the search process, press [Escape] or [Alt+S].
What are the search parameters ? The depth parameter (a number
between 0 and 20) is used by the search algorithm. The bigger it is, the
longer the computer will work. But it will work with much more computed
configurations. To modify this value, firstly, start the " Options " dialogue
box by selecting the " Board+Options " command in the main menu or by pressing
[F5]. Secondly select the " General " tab sheet, and change the depth value.
Most of the time, a small depth (less than 5) is enough to compute a solvable
problem.
Note that if you don't set the " Backtracking " option, then the search
engine will look at all symmetrical problems. (There are 8 symmetries for
a classical board, 6 symmetries for a triangular board, 12 for an hexagonal
one ...). This feature is very important and I advise players not to set
the " Backtracking " option at once, but when the problem still appears
insolvable after you have increased the depth over 6,7 or more.
For a single-vacancy single-survivor problem, if the solution of the
complement problem is present in the set of the final places found, then
Peg Solitaire will display the complement problem solution.
What are the different reasons why a problem is insolvable ?
There can be eleven reasons why the computer claims the problem insolvable
:
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[n°1] n, DeBruijn's first criterion failure.
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[n°2] m, DeBruijn's second criterion failure.
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[n°3] DeBruijn's numbers mismatch between source and target boards.
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[n°4] Not one playable move.
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[n°5] Number of pegs of target <= Number of pegs of source.
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[n°6] Draughtboard criterion failure.
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[n°7] The target board is empty.
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[n°8] Marked pegs must be both in source and target boards.
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[n°9] There can not be only marked pegs on the target board.
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[n°10] Draughtboard criterion failure for inverse problem.
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[n°11] The problem is theoretically possible (according to implemented
criterion) but the computer managed to test all possible moves and has
found that there is no solution.
Saving, Loading and Exporting a solved problem.
Save a problem
Once a problem is resolved, a dialogue box shows. (We call it the "
History " dialogue box). All the solution history appears. Then you can
save this solution by pressing the " Save " button. You have to enter a
character string to name the file.
Load a problem
When the " History " dialogue box is showing, you can load a previously
saved problem. Click on the " Load " button, and select a file. You have
the possibility to see all the saved problems : Start the "Options " dialogue
Box, click on the " De Bruijn's criterion" tab sheet (the third one) and
then, click on the " Solved " or " All " buttons.
Export a problem
If you want to print a solved problem, then use this feature. Click
on the " Export " button that appears when the " History " dialogue box
is showing. You can modify some options like the number of rows or the
text format, simple ASCII or RTF (Rich Text Format). When you select RTF
then you must use an enhanced text editor such like Wordpad (c:\windows\write.exe).
What are all these different numbers ?
n & m
These numbers are computed sums. They are called " De Bruijn's sums
". They are constant for a given board, and keep their value if you correctly
move a peg on the board. If you set one single peg on the board (where
you like), both sums are different from 0. (Except for Lam Turki Board).
So if one of this sum is null on the source board and if your purpose is
to reach a board with only a single peg left, then at once, you can assert
" there is no solution ! ". A famous example is the middle-single vacancy-single
survivor problem on the French board. For this problem, both sums are null.
Using these sums, you can dismiss a great number of potential final places
for the last peg. To see what final places can be considered, select the
" De Bruijn's criterion " tab sheet (the third one) on the " Options "
dialogue box. Red bubbles are showing these possible places. Do note that
" If a solution exists then the last peg must be placed on a hole represented
by a red bubble ".
s,t,m & c
These numbers are cardinals of sets of pegs. All along its life a peg
belongs to the same set, it always keeps member of it, while you play correct
moves. The amount of pegs of a given set decreases during the course of
play; so if the target board has a set with an amount of pegs higher than
the source board then you can claim that the problem is not solvable.
e
This number is called " draughtboard criterion ". When its value is
null, it means that there is not enough of some " inside " pegs of the
board to clear some " outside " pegs. This criterion is used above all
on Continental and French boards.
The two numbers at the left of the main window ?
The first one is the number of left pegs. Second one is the number
of playable moves.
The two numbers on the "History" dialogue box ?
The first one is the number of sweeps. Second one is the longest sweep.
What is a sweep ?
A sweep is a move that captures a specific number of pegs (one or more).
If you are an expert player, it is very interesting to look for " minimum
sweeps " or " maximum longest sweep " problems. Some results are famous,
for instance, considering the English Solitaire, the smallest number of
moves that you can make for the middle " single-vacancy single-survivor
" problem is 18 moves. (For this particular result, a proof has been given
by " Berkeley ", a pseudonym for W. H. Peel).
Dealing with history.
How to cancel the last move ?
Press [BackSpace] key. Or select this command on the " History " menu
items. When you select this command, the last board stored in the " History
" comes to replace the current board.
How to get the starting board ?
Press [Alt+BackSpace] keys. Or select this command on the " History
" menu items. Then the current board get initialized with the source board
that you previously designed or you loaded from a saved problem. When you
select this command, the first board stored in the " History " comes to
replace the current board.
Inverse History, what the use ?
This is a very interesting feature. When you have resolved a problem
(for example, we called " A ", the initial vacant place, and " B " the
final hole) then you have at once a solution for the " inverse problem
" (vacant place " B " and final hole " A "). To see an inverse solution
of a given problem : Once you have resolved the initial problem, close
the " History " dialogue box, select the " Inverse History " command of
the " History " menu (Or press [Alt+Home], and finally re-start the " History
" dialogue box [Alt+Enter] to show the new history. This feature is also
operational for pattern problems. As a very meaningful example : Here is
the initial problem (quite easy to resolve) :
··· ···
·×××· ·····
·×××××· ·······
·××·××· ==> ···×···
·×××××· ·······
·×××· ·····
··· ···
And now, have a look at its inverse problem (a bit more difficult to resolve,
isn't it ?) :
××× ×××
××××× ×···×
××××××× ×·····× This is a famous pattern, historically called :
×××·××× ==> ×··×··× " Le lecteur au milieu de son auditoire "
××××××× ×·····× (" The lecturer in the middle of his audience ")
××××× ×···×
××× ×××
Show History
Press [Alt+Enter] keys. Or select this command from the " History "
menu items. When this dialogue box shows, you can have a look at all moves
you have done or that have been computed.
Registering Peg Solitaire 1.99.
What is shareware ?
" Shareware distribution gives users a chance to try software before
buying it. If you try a Shareware program and continue using it, you are
required to register it. Copyright laws apply to both Shareware and retail
software, and the copyright holder retains all rights, with a few specific
exceptions as stated below. Shareware authors are accomplished programmers,
just like retail authors, and the programs are of comparable quality. (In
both cases, there are good programs and bad ones!) The main difference
is in the method of distribution. The author specifically grants the right
to copy and distribute the software, either to all and sundry or to a specific
group. For example, some authors require written permission before a commercial
disk vendor may copy their Shareware. Shareware is a distribution method,
not a type of software. You should find software that suits your needs
and pocketbook, whether it's retail or Shareware. The Shareware system
makes fitting your needs easier, because you can try before you buy. And
because the overhead is lower, prices are lower also. Shareware has the
ultimate money back guarantee -- if you don't use the product, you don't
pay for it. "
Taken without authorization from Wren-ware Software.
How does it cost ?
If you find Peg Solitaire 1.99 delightful and decide to keep it on
your hard drive, then you must register it. I will send you the last version
of this software, plus other free software of the same quality (also from
myself, like Tetris Pack 1.97 or Sokoban for Windows 95). If you can not
afford such a fee, then have a beer and drink to my health ... yec'hed
mat !
Registration :
To register, print this form, send it with money to:
M. Basciano Philippe
46 rue de Cornouaille
22000 Saint-Brieuc
FRANCE
Peg Solitaire 1.99 : ___ copies at $20,
(or £10, 30DM, 100FF, 15 Euros) each = __________
Add $2 shipping for orders outside EEC = __________
Total payment = __________
Name: _______________________________________
Company: _______________________________________
Address (line 1): _______________________________________
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Electronic Mail address: _______________________________________
Comments:
If you have any comments, write them here ...
Miscallaneous :
Thanks to :
Nicolas Buchon, to have lent his computer to me in order for testing.
Wrenware Software for Shareware information, ...
All of you who have registered your 1.97 or even previous ... version
of Peg Solitaire.
Bibliography :
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John D. Beasley, " The ins and outs of Peg Solitaire ", Oxford Press. 1992.
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Edouard Lucas, " Récréations mathématiques, tome 1
", reprinted by Albert Blanchard library. (Paris). First printed 1879.
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Martin Gardner, " Jeux mathématiques du Scientific American ". reprinted
by Albert Blanchard library. (Paris). First printed 1979.
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Jeanine Cabrera, René Houot, " Traité du jeu du Solitaire
". Ludothèque de l'inpensé radical. Flammarion. 1977.
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Pierre Tougne " Le Solitaire " from " La mathématique des jeux ".
Bibliothèque Pour la Science. 1992.
Various notes
Peg Solitaire is given with more than 300 saved problems. Most of them
(over 95%) have been computed using this version of Peg Solitaire. The
other ones have been solved by hand. (It was necessary to design the problems,
and I did the job, copying problems from printed Solitaire materials and
inventing others). Sometimes, the program found several « Inverse
problems » much more obvious to compute than their initial ones.
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Getting ‘longest sweep’ solution :
An interesting purpose is to look for the last (or last but one) longest
sweep, Peg Solitaire can help a lot. To manage this, I advice players to
design the board that leads to this sweep as target board. (When you have
resolved this, then you can play the final sweep by yourself). You can
also solve the « inverse problem » of this latter. (In most
of cases that gives better results). Following this way, resolving classical
problem « La Corsaire » is very easy. I manage to find solutions
for identical problems on Wiegleb’s Solitaire (with a 16 pegs long sweep
as last but-one sweep) and Continental Solitaire (9 pegs long sweep as
last but-one sweep).
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Fixed peg that finishes the play :
Another objective that can be hunted is to finish the play with a given
peg. Once more, Peg Solitaire can help ! On the target board, you
set this particular peg as marked and you design also the pegs that will
be eaten during the last sweep, ensuring that DeBruijn’s criterion is OK
(both n and m have the same values for source and target boards). Then,
you can run the search process.
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Conclusion :
I think Peg Solitaire 1.99 can help a lot to find any solvable problem.
If you know a solvable problem that Peg Solitaire does not manage to compute
(considering, of course, some minor adjustments like solving the inverse
problem), please let me know ! you will receive a free registered copy
of this great software ...
© May 1999, by Philippe BASCIANO.