# Who Owns the Zebra

A Prolog solver for the ‘Zebra puzzle’ a.k.a. ‘Einstein’s puzzle’.
programming
prolog
puzzles
Author

Aswin van Woudenberg

Published

October 26, 2007

On December 17, 1962, Life International magazine published the following puzzle:

1. There are five houses.
2. The Englishman lives in the red house.
3. The Spaniard owns the dog.
4. Coffee is drunk in the green house.
5. The Ukrainian drinks tea.
6. The green house is immediately to the right of the ivory house.
7. The Old Gold smoker owns snails.
8. Kools are smoked in the yellow house.
9. Milk is drunk in the middle house.
10. The Norwegian lives in the first house.
11. The man who smokes Chesterfields lives in the house next to the man with the fox.
12. Kools are smoked in the house next to the house where the horse is kept.
13. The Lucky Strike smoker drinks orange juice.
14. The Japanese smokes Parliaments.
15. The Norwegian lives next to the blue house.

Now, who drinks water? Who owns the zebra?

In the interest of clarity, it must be added that each of the five houses is painted a different color, and their inhabitants are of different national extractions, own different pets, drink different beverages and smoke different brands of American cigarets.

One other thing: In Statement 6, right means your right.

This puzzle is said to be invented by Einstein and therefore sometimes referred to as Einstein’s puzzle or Einstein’s riddle. Supposedly, he also claimed that only 2% of the world’s population would be smart enough to solve it. For neither claim is there any evidence.

## Solving the puzzle using Prolog

As an example of how to solve these kinds of logic puzzles using Prolog, I wrote this code:

einstein.pl
% A Prolog solver for the Zebra puzzle a.k.a. Einstein's riddle.
% https://en.wikipedia.org/wiki/Zebra_Puzzle

einstein :-
einstein(Solution),
write_sol(Solution).

einstein(Sol) :-
Sol = [
[1,N1,C1,P1,D1,S1],                             % There are five houses.
[2,N2,C2,P2,D2,S2],
[3,N3,C3,P3,D3,S3],
[4,N4,C4,P4,D4,S4],
[5,N5,C5,P5,D5,S5]],
member([_,englishman,red,_,_,_],Sol),               % The Englishman lives in the red house.
member([_,spaniard,_,dog,_,_],Sol),                 % The Spaniard owns the dog.
member([_,_,green,_,coffee,_],Sol),                 % Coffee is drunk in the green house.
member([_,ukrainian,_,_,tea,_],Sol),                % The Ukrainian drinks tea.
member([GH,_,green,_,_,_],Sol),                     % The green house is immediately to the right of the ivory house.
member([IH,_,ivory,_,_,_],Sol),
GH =:= IH + 1,
member([_,_,_,snails,_,old_gold],Sol),              % The Old Gold smoker owns snails.
member([_,_,yellow,_,_,kools],Sol),                 % Kools are smoked in the yellow house.
member([3,_,_,_,milk,_],Sol),                       % Milk is drunk in the middle house.
member([1,norwegian,_,_,_,_],Sol),                  % The Norwegian lives in the first house.
member([BH,_,_,_,_,chesterfields],Sol),             % The man who smokes Chesterfields lives in the house next to the man with the fox.
member([CH,_,_,fox,_,_],Sol),
next_to(BH,CH),
member([DH,_,_,_,_,kools],Sol),                     % Kools are smoked in the house next to the house where the horse is kept.
member([HH,_,_,horse,_,_],Sol),
next_to(DH,HH),
member([_,_,_,_,orange_juice,lucky_strike],Sol),    % The Lucky Strike smoker drinks organge juice.
member([_,japanese,_,_,_,parliaments],Sol),         % The Japanese smokes Parliaments
member([NH,norwegian,_,_,_,_],Sol),                 % The Norwegian lives next to the blue house.
member([BlH,_,blue,_,_,_],Sol),
next_to(NH,BlH),
permutation([englishman,spaniard,ukrainian,japanese,norwegian],[N1,N2,N3,N4,N5]),
permutation([green,ivory,yellow,blue,red],[C1,C2,C3,C4,C5]),
permutation([dog,snails,fox,horse,zebra],[P1,P2,P3,P4,P5]),
permutation([coffee,tea,milk,orange_juice,water],[D1,D2,D3,D4,D5]),
permutation([old_gold,kools,chesterfields,lucky_strike,parliaments],[S1,S2,S3,S4,S5]).

next_to(A,B) :- A =:= B - 1.
next_to(A,B) :- A =:= B + 1.

write_sol(Solution) :-
write('+--+------------+------------+------------+-------------+--------------+'),nl,
maplist(writef('|%2L|%12L|%12L|%12L|%13L|%14L|\n'),Solution),
write('+--+------------+------------+------------+-------------+--------------+'),nl.

The program uses a list of lists to represent the houses and applies a set of constraints to determine the correct answer.

The einstein/1 predicate defines the structure of the solution as a list of lists called Sol. Each sublist corresponds to a house and contains five variables representing the house number, nationality, color, pet, drink, and cigarette brand.

The predicate then uses a set of member/2 and next_to/2 predicates to apply the given clues and constraints to the list of houses. For example, member([_,englishman,red,_,_,_],Sol) specifies that the Englishman lives in the red house, and the predicates member([BH,_,_,_,_,chesterfields],Sol), member([CH,_,_,fox,_,_],Sol), and next_to(BH,CH) specify that the man who smokes Chesterfields lives in the house next to the man with the fox.

Finally, write_sol/1 outputs the solutions in a formatted table.

You can find a copy of this code as a GitHub gist here.

## Running the solver

To run the solver, you first start the Prolog interpreter (I use SWI-Prolog) by opening up a terminal and typing:

swipl