Pynstein

Python tool for solving Einstein (zebra) puzzles using different conditions.

Conditions

To solve the puzzle one can use the following conditions:

• Info-Conditions

  Info-conditions simply discribe a single column, like "The Englishman lives in the red house"

• Position-Conditions

  Position-conditions are just like Info-conditions, but they have a preset column index, e.g. "The Norwegian lives in the first house"

• NextTo-Conditions

  NextTo-conditions mean that two columns are next to each other, regardles of the order, e.g. "The man who smokes Chesterfields lives in the house next to the man with the fox"

• LeftOf/RightOf-Conditions

  LeftOf/RightOf-conditions are like NextTo-condions, but with a difinite order of the columns, e.g. "The green house is immediately to the right/left of the ivory house"

• Distance-Conditions

  Distance conditions ensure that two given columns have a fixed distance to each other, e.g. "A is 3 places left of B"

Exclude conditions

If you want to exclude a certain condition, e.g. "A is NOT left of B", simply use the normal condition "A IS left of B" and pass the additional parameter exclude=True.

Example: puzzle.AddCondition_LeftOf(["A"], ["B"], exclude=True)

Somewhere conditions

For AddCondition_RightOfand AddCondition_LeftOf you can pass the additional parameter somewhere which - if set to True - means that the condition will be met if A is anywhere left of/right of B, not just next to it.

Example: puzzle.AddCondition_LeftOf(["A"], ["B"], somewhere=True)

Note: If wrap-mode is enabled, this will throw an error!

Wrapmode

If you want the grid to be connected ob both ends to form a ring-like structure (e.g. a round table) set wrapmode to true by the following command:

puzzle.Set_Wrap(True)

Usage

Usage is simple. Just pass the conditions, no need to specify the shape of the grid.

For example the classic puzzle taken from the 1962 Life international magazine that looks like the following:

There are five houses.
The Englishman lives in the red house.
The Spaniard owns the dog.
Coffee is drunk in the green house.
The Ukrainian drinks tea.
The green house is immediately to the right of the ivory house.
The Old Gold smoker owns snails.
Kools are smoked in the yellow house.
Milk is drunk in the middle house.
The Norwegian lives in the first house.
The man who smokes Chesterfields lives in the house next to the man with the fox.
Kools are smoked in the house next to the house where the horse is kept.
The Lucky Strike smoker drinks orange juice.
The Japanese smokes Parliaments.
The Norwegian lives next to the blue house.

Now, who drinks water? Who owns the zebra?

Would translate to:

# [nationality, color, animal, drink, brand]
puzzle = Pynstein()

#The Englishman lives in the red house.
puzzle.AddCondition_Info(["Englishman", "red"])

#The Spaniard owns the dog.
puzzle.AddCondition_Info(["Spaniard", None, "dog"])

#Coffee is drunk in the green house.
puzzle.AddCondition_Info([None, "green", None, "coffee"])

#The Ukrainian drinks tea.
puzzle.AddCondition_Info(["Ukrainian", None, None, "tea"])

#The Old Gold smoker owns snails.
puzzle.AddCondition_Info([None, None, "snails", None, "Old Gold"])

#Kools are smoked in the yellow house.
puzzle.AddCondition_Info([None, "yellow", None, None, "Kools"])

#The Lucky Strike smoker drinks orange juice.
puzzle.AddCondition_Info([None, None, None, "orange juice", "Lucky Strike"])

#The Japanese smokes Parliaments.
puzzle.AddCondition_Info(["Japanese", None, None, None, "Parliaments"])

# add position-conditions
#Milk is drunk in the middle house.
puzzle.AddCondition_Position([None, None, None, "milk"], 2)

#The Norwegian lives in the first house.
puzzle.AddCondition_Position(["Norwegian"], 0)

# add nextTo conditions
#The man who smokes Chesterfields lives in the house next to the man with the fox.
puzzle.AddCondition_NextTo([None, None, None, None, "Chesterfields"], [None, None, "fox"])

#Kools are smoked in the house next to the house where the horse is kept.
puzzle.AddCondition_NextTo([None, None, None, None, "Kools"], [None, None, "horse"])

#The Norwegian lives next to the blue house.
puzzle.AddCondition_NextTo(["Norwegian"], [None, "blue"])

# add rightOf conditions
#The green house is immediately to the right of the ivory house.
puzzle.AddCondition_RightOf([None, "green"], [None, "ivory"])

# add missing informations
puzzle.AddCondition_Info([None, None, None, "water"])
puzzle.AddCondition_Info([None, None, "zebra"])

puzzle.Solve()
print(puzzle.Solutions)

Note that unknown fields must be None. Trailing None-fields can be dropped.

The full example can be seen under example.py