# Lorin Hochstein

Ramblings about software, research and other things

## “Who owns the fish” in Alloy

with one comment

Hacker News linked to a logic puzzle with the following constraints:

There are five houses in five different colors starting from left to right. In each house lives a person of a different nationality. These owners all drink a certain type of beverage, smoke a certain brand of cigarette and keep a certain type of pet. No two owners have the same pet, smoke the same brand or drink the same beverage. The question is: WHO OWNS THE FISH??? Hints:

1. The Brit lives in the red house
2. The Swede keeps dogs as pets
3. The Dane drinks tea
4. The green house is on the left of the white house
5. The green house’s owner drinks coffee
6. The person who smokes Pall Mall rears birds
7. The owner of the yellow house smokes Dunhill
8. The man living in the centre house drinks milk
9. The Norwegian lives in the first house
10. The person who smokes Marlboro lives next to the one who keeps cats
11. The person who keeps horses lives next to the person who smokes Dunhill
12. The person who smokes Winfield drinks beer
13. The German smokes Rothmans
14. The Norwegian lives next to the blue house
15. The person who smokes Marlboro has a neighbor who drinks water

Alloy is very well-suited to solving this type of problem, so I gave it a go. Here’s what my Alloy model looks like:

```open util/ordering[House]

sig House {
color: one Color
}

abstract sig Person {
occupies: one House,
drinks: one Beverage,
smokes: one Cigarette,
keeps: one Pet
}
one sig Brit, Swede, Dane, Norwegian, German extends Person {}

abstract sig Color {}
one sig White, Yellow, Blue, Red, Green extends Color {}

abstract sig Beverage {}
one sig Tea, Coffee, Milk, Beer, Water extends Beverage {}

abstract sig Pet {}
one sig Birds, Cats, Dogs, Horses, Fish extends Pet {}

abstract sig Cigarette {}
one sig PallMall, Dunhill, Marlboro, Winfield, Rothmans extends Cigarette {}

fact allRelationsAreOneToOne {
color.~color in iden
occupies.~occupies in iden
drinks.~drinks in iden
smokes.~smokes in iden
keeps.~keeps in iden
}

pred problemConstraints {

// The Brit lives in the red house
Red in Brit.occupies.color

//The Swede keeps dogs as pets
Dogs in Swede.keeps

// The Dane drinks tea
Tea in Dane.drinks

// The green house is on the left of the white house
Green in prev[color.White].color

// The green house's owner drinks coffee
Coffee in (occupies.(color.Green)).drinks

// The person who smokes Pall Mall rears birds
Birds in (smokes.PallMall).keeps

// The owner of the yellow house smokes Dunhill
Dunhill in (occupies.(color.Yellow)).smokes

// The man living in the centre house drinks milk
(drinks.Milk).occupies in first[].next.next

// The Norwegian lives in the first house
Norwegian in occupies.first[]

// The person who smokes Marlboro lives next to the one who keeps cats
(smokes.Marlboro).occupies in (keeps.Cats).occupies.(next + prev)

// The person who keeps horses lives next to the person who smokes Dunhill
(keeps.Horses).occupies in (smokes.Dunhill).occupies.(next + prev)

// The person who smokes Winfield drinks beer
Beer in (smokes.Winfield).drinks

// The German smokes Rothmans
German in smokes.Rothmans

// The Norwegian lives next to the blue house
Blue in Norwegian.occupies.(next+prev).color

// The person who smokes Marlboro has a neigbor who drinks water
(drinks.Water).occupies in (smokes.Marlboro).occupies.(next+prev)

}

run problemConstraints for exactly 5 House```

Alloy’s “Magic Layout” did a surprisingly good job at displaying the results. I had to manually rearrange the output so the houses would be displayed in the correct order, but otherwise no fiddling was required. Here’s what it looks like:

I also put it up on Github.