# ZEBRA, Who Owns the Zebra?
# Adapted from GLPK to pymprog by Yingjie Lan <ylan@pku.edu.cn>
########################################################################
# The Zebra Puzzle is a well-known logic puzzle.
#
# It is often called "Einstein's Puzzle" or "Einstein's Riddle"
# because it is said to have been invented by Albert Einstein as a boy,
# with the common claim that Einstein said "only 2 percent of the
# world's population can solve". It is also sometimes attributed to
# Lewis Carroll. However, there is no known evidence for Einstein's or
# Carroll's authorship.
#
# There are several versions of this puzzle. The version below is
# quoted from the first known publication in Life International
# magazine on December 17, 1962.
#
# 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 cigarettes. One
# other thing: In statement 6, right means your right.
#
# (From Wikipedia, the free encyclopedia.)
########################################################################
HOUSE=range(1,6)
COLOR = ("blue", "green", "ivory", "red", "yellow")
NATIONALITY = ("Englishman", "Japanese", "Norwegian",
"Spaniard", "Ukranian")
DRINK = ("coffee", "milk", "orange_juice", "tea", "water")
SMOKE = ("Chesterfield", "Kools", "Lucky_Strike",
"Old_Gold", "Parliament")
PET = ("dog", "fox", "horse", "snails", "zebra")
from pymprog import *
#Uncomment to forbid comparison with a variable as an expression.
#pymprog.variable.comparable=False
zeb = model("zebra")
color=zeb.var('color', iprod(HOUSE, COLOR), bool)
for h in HOUSE: sum(color[h,c] for c in COLOR)==1
for c in COLOR: sum(color[h,c] for h in HOUSE)==1
nationality=zeb.var('nation', iprod(HOUSE, NATIONALITY), bool)
for h in HOUSE: sum(nationality[h,n] for n in NATIONALITY)==1
for n in NATIONALITY: sum(nationality[h,n] for h in HOUSE)==1
drink=zeb.var('drink', iprod(HOUSE, DRINK), bool)
for h in HOUSE: sum(drink[h,d] for d in DRINK)==1
for d in DRINK: sum(drink[h,d] for h in HOUSE)==1
smoke=zeb.var('smoke',iprod(HOUSE, SMOKE),bool)
for h in HOUSE: sum(smoke[h,s] for s in SMOKE)==1
for s in SMOKE: sum(smoke[h,s] for h in HOUSE)==1
pet=zeb.var('pet', iprod(HOUSE, PET),bool)
for h in HOUSE: sum(pet[h,p] for p in PET)==1
for p in PET: sum(pet[h,p] for h in HOUSE)==1
## the Englishman lives in the red house */
for h in HOUSE: nationality[h,"Englishman"]==color[h,"red"]
## the Spaniard owns the dog */
for h in HOUSE: nationality[h,"Spaniard"]==pet[h,"dog"]
## coffee is drunk in the green house */
for h in HOUSE: drink[h,"coffee"]==color[h,"green"]
## the Ukrainian drinks tea */
for h in HOUSE: nationality[h,"Ukranian"]==drink[h,"tea"]
## the green house is immediately to the right of the ivory house */
for h in HOUSE:
color[h,"green"] == (color[h-1, "ivory"] if h>1 else 0)
## the Old Gold smoker owns snails */
for h in HOUSE: smoke[h,"Old_Gold"]==pet[h,"snails"]
## Kools are smoked in the yellow house */
for h in HOUSE: smoke[h,"Kools"]==color[h,"yellow"]
## milk is drunk in the middle house */
drink[3,"milk"] == 1
## the Norwegian lives in the first house */
nationality[1,"Norwegian"] == 1
# the man who smokes Chesterfields lives in the house
# next to the man with the fox */
for h in HOUSE:(
1 - smoke[h,"Chesterfield"] +
(0 if h == 1 else pet[h-1,"fox"]) +
(0 if h == 5 else pet[h+1,"fox"]) >= 1 )
# Kools are smoked in the house next to the house
# where the horse is kept */
for h in HOUSE:(
1 - smoke[h,"Kools"] +
(0 if h == 1 else pet[h-1,"horse"]) +
(0 if h == 5 else pet[h+1,"horse"]) >= 1)
## the Lucky Strike smoker drinks orange juice */
for h in HOUSE:
smoke[h,"Lucky_Strike"] == drink[h,"orange_juice"]
## the Japanese smokes Parliaments */
for h in HOUSE:
nationality[h,"Japanese"] == smoke[h,"Parliament"]
#zeb.verb = True
## the Norwegian lives next to the blue house */
for h in HOUSE:(
1 - nationality[h,"Norwegian"] +
(0 if h == 1 else color[h-1,"blue"]) +
(0 if h == 5 else color[h+1,"blue"]) >= 1)
zeb.solve()
def answ(h):
for c in COLOR:
if color[h,c].primal>0: break
for n in NATIONALITY:
if nationality[h,n].primal>0: break
for d in DRINK:
if drink[h,d].primal>0: break
for s in SMOKE:
if smoke[h,s].primal>0: break
for p in PET:
if pet[h,p].primal>0: break
return (h,c,n,d,s,p)
print("HOUSE COLOR NATIONALITY DRINK SMOKE PET")
for h in HOUSE:
print("%5d %-6s %-11s %-12s %-12s %-6s"%answ(h))
zeb.end()
