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Solving the "Who has a fish?" Puzzle or "Who has fish?" on the PROLOGUE.

Lecture



There is a puzzle that was invented by A. Einstein. He argued that only 2% of people can solve this problem. It also says that 2% of people solve this problem at about the same time. I was intrigued, but did I enter into this 2%. I looked at the conditions, noticed the time, and ... 25 minutes was spent on solving the problem. I wonder how much the computer will think? Made a program on the PROLOGUE, launched ... tired of waiting. I could not even check whether it works correctly? After reading the site carefully, I realized that it would be very long for a simple search. And why did I decide much faster? I began to analyze the course of my thoughts when solving a puzzle. And then, in the likeness of his thoughts, he created an algorithm, and then the program itself on the PROLOGUE, which solves this problem. Creating a program took a whole day. But she gave the decision in 0.5 seconds!

Conditions of the problem.
1. There are 5 houses each in a different color.
2. In each house lives one person, different from the neighboring nationality: German, English, Swede, Dane, Norwegian.
3. Everyone drinks only one specific drink, smokes a certain brand of cigarettes and holds a certain animal.
4. None of the 5 people drinks the same as other drinks, does not smoke the same cigarettes and does not keep the same animal.
Question: Who owns the fish?
Tips:
1. The Englishman lives in the red house.
2. The Swede keeps the dog.
3. Dane drinking tea.
4. The green house stands to the left of the white.
5. A resident of the green house drinks coffee.
6. The person who smokes Pall Mall is holding a bird.
7. A resident from an average home drinks milk.
8. A yellow house dweller smokes Dunhill.
9. Norwegian lives in the first house.
10. The smoker Marlboro lives about the one who holds the cat.
11. The man who holds the horse lives near the one who smokes Dunhill.
12. Cigarette smoker Winfield drinks beer.
13. The Norwegian lives near the blue house.
14. German smokes Rothmans.
15. The Marlboro smoker lives next door to a person who drinks water.
Below is a program to solve the puzzle.

  / * 
  puzzle solution example 
  who has fish?  (Who has a fish?) 
  Author: Ermolaev D.S.  www.icreator.ru 
  There are five colorful houses in which different people live, 
  who drink different drinks 
  and who have different animals and who smoke different cigarettes. 
  need to answer the question with 15 tips 
  Who has fish? 
  Here is a quick way to find a solution. 
  * / 
  domains 
  Color = yellow;  blue;  red;  green;  white 
  House number = first;  second;  third;  fourth;  fifth 
  % reference - here indicates the ability to work with null values 
  Home Tag = reference tag (Color, House Number) 
  Nationality = Norwegian;  Dane;  Englishman;  German;  Swede 
  Drink = water;  tea;  milk;  coffee;  beer 
  Cigarettes = dunhill;  marlboro;  pall_mall;  rothmans;  winfield 
  Animal = cat;  horse;  bird;  a fish;  dog 
  House = reference house (Sign House, Nationality, Drink, Cigarettes, Animal) 
  Houses = reference House * 
  Value = q (Color);  Nd (House number);  nts (nationality); 
  np (Beverage);  sg (cigarettes);  ww (animal) 
  Values ​​= Value * 

 
  predicates 
  nondeterm color (Color) 
  nondeterm nationality (Nationality) 
  nondeterm drink (Beverage) 
  nondeterm cigarettes (Cigarettes) 
  nondeterm animal (Animal) 
  nondeterm house (Number, Sign Home, Nationality, Drink, Cigarettes, Animal) 
  nondeterm house_name (SignHome, Nationality, Drink, Cigarettes, Animal) 
  nondeterm condition (Number, House, Homes) 
  conditions not broken (Room, House, House) 
  % without "left" - "right" 
  nondeterm houses (order, houses, house, house nearby) 
  % subject to "left" - "right" 
  nondeterm houses_fitted (Houses, House, House Nearby) 
  nondeterm near (House Number, House Number) 
  nondeterm adjoins (House number Left, House number Right) 
  house_non-unicorn1 (House, House) 
  House_Neuniquelen (House, Houses) 
  compare_values ​​(House, Values, House, Values) 
  value_connected (Value) 

 
  clauses 
  % definition of possible values 
  % explicit definition helps during debugging 
  % catch errors in values 
  yellow color).  blue color).  color (red).  Green colour).  White colour). 
  nationality (Norwegian).  nationality (Dane). 
  nationality (Englishman).  nationality (German).  nationality (Swede). 
  drink (water).  drink (tea).  drink (milk).  drink (coffee).  drink (beer). 
  cigarettes (dunhill).  cigarettes (marlboro).  cigarettes (pall_mall). 
  cigarettes (rothmans).  cigarettes (winfield). 
  animal (cat).  animal (horse).  animal (bird). 
  animal (fish).  animal (dog). 

 
  % 
  % basic task conditions 
  % 
  %one.  An Englishman lives in a red house. 
  house (1, tag (red, _), English, _, _, _). 
  % 2.  Swede contains a dog. 
  house (2, _, swede, _, _, dog). 
  % 3.  Dane drinking tea. 
  house (3, _, Dane, tea, _, _). 
  %five.  the tenant of the green house drinks coffee. 
  house (5, tag (green, _), _, coffee, _, _). 
  % 6.  the one who smokes Pall Mall contains a bird. 
  house (6, _, _, _, pall_mall, bird). 
  % 7.  who lives in the average (third) house drinks milk. 
  house (7, sign (_, third), _, milk, _, _). 
  %eight.  he who lives in the yellow house smokes Dunhill. 
  house (8, tag (yellow, _), _, _, dunhill, _). 
  %9.  in the first house lives a Norwegian. 
  house (9, tag (_, first), Norwegian, _, _, _). 
  % 12 Winfield cigarette smoker drinks beer. 
  house (12, _, _, beer, winfield, _). 
  % 14 German Rothmans smoke. 
  house (14, _, German, _, rothmans, _). 

 
  % this condition - that you can take any value - if it is not yet connected 
  dom_nabum (sign (Color, _), Nat, Nap, Sig, Alive): - 
  color (Color), nationality (Nat), 
  drink (nap), cigarettes (sig), animal (alive). 

 
  % condition-dependency, here the check is done immediately for both houses 
  %four.  the green house is to the left of the white 
  Condition (4, HomeGreen, Homes): - 
  HomeGreen = Home (tag (green, _), _, _, _, _), 
  not (non_uniquelen (homegreen, houses)), 
  houses_fitted (Houses, HomeGreen, HouseWhite), 
  Home White = home (tag (white, _), _, _, _, _), 
  not (dom_ununikalen (HomeWhite, Homes)). 
  %ten.  the Marlboro smoker lives next to the one who keeps the cat. 
  condition (10, House, Houses): - House = house (_, _, _, marlboro, _), 
  not (non_uniquelen home (House, Houses)), 
  home_s (Houses, Home, HomeRyad), 
  DomNadom = house (_, _, _, _, cat), 
  not (non_uniquelen (DomRyad, Home)). 
  %eleven.  one who has a horse lives next to one who smokes Dunhill. 
  condition (11, House, Houses): - House = house (_, _, _, _, horse), 
  not (non_uniquelen home (House, Houses)), 
  home_s (Houses, Home, HomeRyad), 
  DomNear = house (_, _, _, dunhill, _), 
  not (non_uniquelen (DomRyad, Home)). 
  % 13 Norwegian lives near the blue house. 
  condition (13, House, Houses): - House = house (_, Norwegian, _, _, _), 
  not (non_uniquelen home (House, Houses)), 
  home_s (Houses, Home, HomeRyad), 
  DomNear = house (sign (blue, _), _, _, _, _), 
  not (non_uniquelen (DomRyad, Home)). 
  % 15 Smoker Marlboro lives next door to a person who drinks water. 
  condition (15, House, Houses): - House = house (_, _, _, marlboro, _), 
  not (non_uniquelen home (House, Houses)), 
  home_s (Houses, Home, HomeRyad), 
  DomNear = house (_, _, water, _, _), 
  not (non_uniquelen (DomRyad, Home)). 
  % condition for access to simple facts 
  condition (Nome, House, Homes): - 
  house (Nome, N, Nat, Nap, Sig, Alive), 
  Home = home (P, Nat, Nap, Sig, Alive), 
  not (dom_newunikalen (House, Houses)). 

 
  % 
  % now the conditions for validation 
  % 
  % condition-dependency, here the check is done immediately for both houses 
  % here is not exactly the condition 
  % so that all conditions are checked 
  % 4. the green house is to the left of the white 
  conditions not broken (4, Homegreen, Houses): - 
  HomeGreen = home (sign (Color, _), _, _, _, _), 
  (color), 
  Color = green, 
  Home White = home (tag (white, _), _, _, _, _), 
  not (houses_single (Houses, HomeGreen, HomeWhite)), 
  fail. 
  %ten.  the Marlboro smoker lives next to the one who keeps the cat. 
  conditions are not violated (10, House, Houses): - House = house (_, _, _, Cig, _), 
  bound (sig) 
  Sig = marlboro, 
  DomNadom = house (_, _, _, _, cat), 
  not (home_unit (Home, House, HomeOrD)), 
  fail. 
  %eleven.  the one who has the horse lives next to the one who smokes Dunhill. 
  conditions are not violated (11, House, Houses): - House = house (_, _, _, _, Alive), 
  bound (Alive) 
  Alive = horse 
  DomNear = house (_, _, _, dunhill, _), 
  not (home_unit (Home, House, HomeOrD)), 
  fail. 
  % 13 Norwegian lives near the blue house. 
  conditions are not violated (13, House, Houses): - House = house (_, Nat, _, _, _), 
  bound (nat) 
  Nat = Norwegian 
  DomNear = house (sign (blue, _), _, _, _, _), 
  not (home_unit (Home, House, HomeOrD)), 
  fail. 
  % 15 Smoker Marlboro lives next door to a person who drinks water. 
  conditions are not violated (15, House, Houses): - House = house (_, _, _, Sig, _), 
  bound (sig) 
  Sig = marlboro, 
  DomNear = house (_, _, water, _, _), 
  not (home_unit (Home, House, HomeOrD)), 
  fail. 
  % check for simple fact conditions 
  conditions are not violated (0, Home, _): - 
  % take the values ​​of the checked house 
  House = house (sign (Color, Number), Nat, Nap, Whitefish, Alive), 
  % take the values ​​of the conditional fact 
  home (_, sign (Color1, Number1), Nat1, Nap1, Cig1, Alive1), 
  % if values ​​from one list are related and 
  % from another too - they should be equal 
  % Otherwise the condition is not met. 
  not (compare_values ​​( 
  House, 
  [t (Color), nd (Number), nts (Nat), np (Nap), sg (Cig), Livestock (Alive)], 
  house (sign (Color1, Number1), Nat1, Nap1, Cig1, Alive1), 
  [ts (Tsvet1), nd (Number 1), nts (Nats1), np (Nap1), sg (Sig1), zhv (Alive1)]) 
  ), 
  fail. 
  % if it came here, then 
  % all conditions are met 
  conditions are not violated (0, _, _): - !. 

 
  value_connected (v (Value)): - bound (Value),!. 
  value_connected (LD (Eq)): - bound (Value),!. 
  value_connected (nc (zn)): - bound (zn),!. 
  value_connected (np (Value)): - bound (Value),!. 
  value_connected (cr (Value)): - bound (Value),!. 
  value_connected (eq (zn)): - bound (zn),!. 

 
  % verification of relationships in simple conditions-facts 
  compare_values ​​(Home, [What | _], Home1, [What1 | _]): - 
  value_ is related (What), 
  value_connected (What1), 
  What = What1, 
  % if something matched, then everything else should match 
  !% so there is a prohibition of rollback 
  House = House1, 
  ! 
  compare_values ​​(House, [_ | Ost], House1, [_ | Ost1]): - 
  % take the next couple of values 
  compare_values ​​(House, Ost, Dom1, Ost1), 
  ! 
  check_values ​​(_, [], _, []): - 
  % comparison successful 
  ! 

 
  % do not compare with yourself 
  house_ is not unique1 (house (sign (_, Number1), _, _, _, _), 
  house (sign (_, Number2), _, _, _, _)): - Number1 = Number2, 
  fail. 
  % if both values ​​are related and equal 
  house_ is not unique1 (house (sign (What, _), _, _, _, _), house (sign (What1, _), _, _, _, _)): - 
  bound (What), bound (What1), What = What1, 
  ! 
  house_ is not unique1 (house (_, what, _, _, _), house (_, what1, _, _, _)): - 
  bound (What), bound (What1), What = What1, 
  ! 
  house_ is not unique1 (house (_, _, what, _, _), house (_, _, what1, _, _)): - 
  bound (What), bound (What1), What = What1, 
  ! 
  house_non-unicorn1 (house (_, _, _, what, _), house (_, _, _, what1, _)): - 
  bound (What), bound (What1), What = What1, 
  ! 
  house_ is not unique1 (house (_, _, _, _, what), house (_, _, _, _, what1)): - 
  bound (What), bound (What1), What = What1, 
  ! 
  % 
  % check on the condition of uniqueness: all values ​​at home 
  % must be unique 
  % 
  dom_nunikalen (dom, [domDrugoy | _]): - 
  house_non-unicorn1 (House, HouseOther), 
  ! 
  dom_newunikalen (dom, [_ | dom]): - 
  dom_nunikalen (House, Houses), 
  ! 

 
  % definition of general rules for the location of houses 
  Near (Place, Near): - adjacent (Place, Near). 
  Near (Place, Near): - adjacent (Near, Place). 
  adjacent (first, second). 
  adjacent (second, third). 
  adjacent (third, fourth). 
  adjacent (fourth, fifth). 

 
  % definition of the house next to the data without left-right 
  home_circuit ([HomeBank | _], home (sign (_, Place), _, _, _, _), HomeBank): - 
  DomNear = house (sign (_, Near), _, _, _, _) 
  near (Place, Near). 
  home_number ([_ | Houses], Home, HomeOrD): - 
  home_s (Houses, Home, HomeRyad), 
  ! 
  % definition of the house next to the data given the left-right 
  houses_single ([HomeDeath | _], home (sign (_, Place), _, _, _, _), HomeDeck): - 
  DomNear = house (sign (_, Near), _, _, _, _) 
  adjacent (Location, Nearby). 
  houses_single ([_ | Houses], House, DomBank): - 
  houses_fitted (Houses, House, HouseBefore), 
  ! 

 
  predicates 
  all_connected1 (House) 
  all_connected (Houses) 
  not_connected1 (House) 
  nondeterm is not related (Home, House) 

 
  clauses 
  all_connected1 (house (P, H, Nap, Sig, G)): - bound (P), bound (N), bound (Nap), 
  bound (sig), bound (Ж),!. 
  % Is everything solved? 
  all_connected ([Home | Houses]): - 
  ! 
  all_connected1 (House), 
  all_connected (Houses) 
  ! 
  all_connected ([]): - !. 

 
  un_connected1 (house (sign (What, _), _, _, _, _)): - free (What),!. 
  un_connected1 (house (_, What, _, _, _)): - free (What),!. 
  un_connected1 (house (_, _, what, _, _)): - free (what),!. 
  un_connected1 (house (_, _, _, What, _)): - free (What),!. 
  un_connected1 (house (_, _, _, _, what)): - free (what),!. 

 
  % find a house that has unrelated values 
  Unbound ([Home | _], Home): - 
  not_connected1 (House). 
  Unrelated ([_ | Houses], Home): - 
  Unrelated (Houses, House). 

 
  predicates 
  nondeterm select_explicit_number (Number) 
  nondeterm solve2 (House, Homes, Room) 
  all_conditions_used (rooms, houses) 
  nondeterm remember_selection (House, House) 
  condition_handled (Number, Numbers) 
  nondeterm solve1 (Houses, Rooms) 
  nondeterm finish out (Home) 
  solve (at home) 

 
  clauses 
  % choose such conditions and connections - which are clearly 
  % follow current data and conditions 
  % it speeds up the decision 
  select_explicit_number (Nom): - 
  condition (Nome, Home, []), 
  Home = home (tag (_, Number), _, _, _, _), 
  % If a number linking occurred, then it is explicit! 
  bound (Number). 
  % if some condition worked, 
  % you need to remember its result in the general list 
  remember_select (Home, [Home | _]). 
  remember_select (Home, [_ | Home]): - 
  remember_selection (House, Houses). 

 
  % checks if such a condition has already been processed 
  condition_handled (Nome, [Nom | _]): - !. 
  condition_handled (Nome, [_ | Processed]): - 
  condition_handled (Nome, Processed), 
  ! 

 
  % choice of conditions 
  solve2 (House, AllHouses, Nome): - 
  % to speed up the decision - the choice of the best conditions. 
  % using this predicate execution is less than 0.5 seconds, 
  % without this predicate - runtime on ORDERS is more! 
  select_explicit_connection (Nom), 
  condition (Nome, Home, All Homes). 
  solve2 (House, AllHouses, Nome): - 
  % enumeration of all conditions 
  condition (Nome, Home, All Homes). 

 
  % check - are all conditions used 
  all_conditions_used (Processed, Home): - 
  condition (Number, _, Home), 
  not (condition_handled (Number, Processed)) 
  fail. 
  all_conditions_used (_, _): -!. 

 
  % applies all the conditions of the problem and returns the received 
  % result for further binding 
  Solve1 (All Homes, Processed): - 
  % if all rules are used, then exit and give the result 
  % for further selection at random 
  all_conditions_used (Processed, AllHouses), 
  ! 
  Solve1 (All Homes, Processed): - 
  % use the condition of the problem 
  decide2 (House, AllHouses, Nome), 
  % this condition has not yet been processed 
  not (condition_handled (Nom, Processed)), 
  % remember the result of the condition 
  % here if there is a rollback below, then the assignment 
  % can be done for other homes 
  remember_select (House, AllHouses), 
  % if the house is unique 
  not (non_uniquelen home (House, AllHouses)), 
  % and not others violated the conditions of the problem 
  conditions are not violated (_, House, All Houses), 
  % then move on 
  Solve1 (All Homes, [Nom | Processed]). 

 
  The% remaining unbound values ​​will bind based on 
  % condition that values ​​should not be repeated 
  % that is, you can take any possible value 
  % and insert it if the conditions of the problem are not violated 
  finish out (All House): - 
  % take a house that has unrelated value 
  not_connected (AllHouses, House), 
  House = house (P, N, Nap, Sig, Alive), 
  % choose this value randomly 
  dom_nabum (P, N, Nap, Sig, Alive), 
  % check the condition of uniqueness 
  not (non_uniquelen home (House, AllHouses)), 
  % and at the same time all the conditions of the problem are true 
  conditions are not violated (_, House, All Houses), 
  % search for another unrelated value 
  finish out (All House). 
  finish (House): - 
  % if everything is already decided (connected), then the output 
  all_connected (Houses) 
  ! 

 
  solve (Home): - 
  Houses = [house (sign (_, first), _, _, _, _), 
  house (sign (_, second), _, _, _, _), 
  house (sign (_, third), _, _, _, _), 
  house (sign (_, fourth), _, _, _, _), 
  house (sign (_, fifth), _, _, _, _)], 
  % processing conditions 
  % here all conditions must be met (applied) 
  solve1 (Houses, []), 
  % remaining unbound values ​​needed 
  % tie at random with a condition check 
  to finish (House), 
  ! 

 
  Goal: - 
  marktime (0, T1), 
  solve (at home) 
  marktime (0, T2), 
  difftime (T2, T1, Toast), 
  nl, write (Home, ":", Toast). 

Perhaps the program will seem pretty tricked out to you, but it is precisely such actions a person performs when solving this puzzle.


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