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The Winnability of Klondike Solitaire and Many Other Patience Games [article]

Charlie Blake, Ian P. Gent
2019 arXiv   pre-print
Klondike is just one of many single-player card games, generically called 'patience' or 'solitaire' games, for which players have long wanted to know how likely a particular game is to be winnable.  ...  Our ignorance of the winnability percentage of the game in the Windows Solitaire program, more properly called 'Klondike', has been described as "one of the embarrassments of applied mathematics".  ...  We thank those who have helped us in our work on patience, including Matt Birrell, Dawn Black, Laura Brewis, Art Cabral, Nguyen Dang, Shlomi Fish, Jordina Francès de Mas, Chris Jefferson, Donald Knuth,  ... 
arXiv:1906.12314v3 fatcat:4cp2plsb6bglbpcc3et6w2oh5q

Caching Search States in Permutation Problems [chapter]

Barbara M. Smith
2005 Lecture Notes in Computer Science  
Caching states visited has proved effective in reducing both search effort and run-time for difficult instances of each class, and the space requirements are manageable.  ...  However, we show that for some problems recording assignments is useful, because other assignments can lead to the same state of the search.  ...  This material is based on works supported by the Science Foundation Ireland under Grant No. 00/PI.1/C075.  ... 
doi:10.1007/11564751_47 fatcat:e6fhz3hshfbefdxkvq6geuoqru

Page 316 of Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting Vol. 91, Issue 7 [page]

1921 Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting  
By infinite patience, waiting at water- holes, or lying motionless in the shadow of isolated little bushes, a closer ac- quaintance may be had with the game. THE DESERT.  ...  If nothing is found, likely grazing grounds in the vicinity should be visited and searched for tracks fresh enough to be worth follow- ing up. In the evening game may be met with coming in to water.  ... 

Page 204 of Photo-Era Magazine : The American Journal of Photography Vol. 54, Issue 4 [page]

1925 Photo-Era Magazine : The American Journal of Photography  
Raccoons are to be found along water-courses in search of food. Beaver are hard to get in action and their homes are remote from civilisation.  ...  A photographer experienced in wild game- habits directs that one should locate the accus- tomed habitat of the animals and build a blind two days before making the pictures so that they will get accustomed  ... 

Page 107 of The New Monthly Magazine Vol. 67, Issue 265 [page]

1842 The New Monthly Magazine  
—I crossed the river this morning in search of new ground ; for the antelope near our encampment now know my green coat 60 well, that it no sooner appears upon the plain, than every one makes off, as if  ...  My brother’s horse was in one of his fidgety moods, fretting and bucking like a goat, till at last he lost patience, and seeing the buck that hed baffled us trotting along with a very supercilious air,  ... 

Auto-tabling for subproblem presolving in MiniZinc

Jip J. Dekker, Gustav Björdal, Mats Carlsson, Pierre Flener, Jean-Noël Monette
2017 Constraints  
In order to encourage modellers to try tabling, we extend the MiniZinc toolchain to perform the automatic tabling of suitably annotated predicate definitions, without requiring any changes to solvers,  ...  thereby eliminating both the tedium and the obfuscation.  ...  Example 1 To illustrate the idea, consider the patience game Black Hole [27] .  ... 
doi:10.1007/s10601-017-9270-5 fatcat:ybvvxytgsbebrjxyv67lo4kwqu

Automatic Discovery and Exploitation of Promising Subproblems for Tabulation [chapter]

Özgür Akgün, Ian P. Gent, Christopher Jefferson, Ian Miguel, Peter Nightingale, András Z. Salamon
2018 Lecture Notes in Computer Science  
The process of discovering promising subproblems and tabulating them is entirely automated in the tool Savile Row. A cache is implemented to avoid tabulating equivalent subproblems many times.  ...  We demonstrate good performance on the benchmark problems used in earlier work on tabulation, and also for several new problem classes.  ...  Black Hole Black Hole is a patience card game where cards are played one by one into the 'black hole' from seventeen face-up fans of three cards. All cards can be seen at all times.  ... 
doi:10.1007/978-3-319-98334-9_1 fatcat:75g7q4brcbdpng6febatib6e6u

Conditional Symmetry Breaking [chapter]

Ian P. Gent, Tom Kelsey, Steve A. Linton, Iain McDonald, Ian Miguel, Barbara M. Smith
2005 Lecture Notes in Computer Science  
We introduce the study of Conditional symmetry breaking in constraint programming.  ...  These are: adding conditional symmetry-breaking constraints, reformulating the problem to remove the symmetry, and augmenting the search process to break the conditional symmetry dynamically through the  ...  The Patience/Solitaire game 'Black Hole' We now show the value of conditional symmetries in a case study of the game 'Black Hole'. Different approaches to solving this game are described in [7] .  ... 
doi:10.1007/11564751_21 fatcat:lvxwh2aaqfgkjdfwr3cicdgjp4

Page 639 of Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting Vol. 93, Issue 11 [page]

1923 Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting  
Like my old black setter Boss he never required a lesson in the field. I have sometimes wondered if the black color had anything to do with it.  ...  The eggs were taken away and the nest broken up. I have always been sorry that he was not allowed to complete the incubation. Among other fowls I had a black-breasted game cock and three hens.  ... 

Page 235 of The Aldine: The Art Journal of America Vol. 5, Issue 12 [page]

1872 The Aldine: The Art Journal of America  
The training of dogs requires patience as well as time, for they are apt, at first, to be drawn from the game by any small creature that may present itself, and are also liable to bite the game too hard  ...  The search continuing, the girl found in a corner, under the bed, sevenpence Dandie ithat is—beg for money, and not for food.  ... 

Page 244 of Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting Vol. 96, Issue 4 [page]

1926 Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting  
Practical Game Breeding (Continued from page 221) the little chicks. Men are usually too feeble in the quality and quantity of patience to be able to manage this part of game breeding.  ...  Every rat, weasel, mink, com- ing on your premises to investigate the delicious odor of new, young game birds will run behind these boards in search- ing for hiding places.  ... 

Page 727 of The Congregationalist and Herald of Gospel Liberty Vol. 85, Issue 20 [page]

1900 The Congregationalist and Herald of Gospel Liberty  
a mile or two in making the round is a joy, never a weariness, because of the object in view and the mind’s exhilaration. ‘ On the “ putting green ’’ coolness, patience, caution, precision come inte.  ...  The rules of the game require also the observance of many little courtesies, a training in which is not wholly needless in the case of clergymen. Brethren, play golf!  ... 

Page 103 of Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting Vol. 25, Issue 6 [page]

1885 Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting  
It belongs to the genus Sphes, and its nests are placed in holes in the ground, which it excavates with much care and patience.  ...  room, evidently in search of something.  ... 

Page 117 of All the Year Round Vol. 10, Issue 231 [page]

1863 All the Year Round  
Knox describes from personal observation, how the heron, spider-like in his patience in watching for his prey, and cat-like in his activity in securing it, catches the water-rat when cross- ing a brook  ...  A Scottish observer describes three or four of them as standing weird-like in a ploughed field, where they were on the look- out for such game as it might yield them.  ... 

Page 319 of Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting Vol. 28, Issue 15 [page]

1887 Forest and Stream; A Journal of Outdoor Life, Travel, Nature Study, Shooting, Fishing, Yachting  
My purpose in going through the Park was to see its win- ter features and to learn something about the game there. This I have done. I can only give estimates in regard to the game.  ...  The “gopher” is a variety of land turtle which remains in its hole dor- mant during the winter.  ... 
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