Einstein quiz

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The Einstein quiz is a logic puzzle.

Question

How to solve the Einstein quiz [1] and similarly structured problems using R-tools?

Facts:

• There are 5 houses in 5 different colors.
• In each house lives a person with a different nationality.
• These 5 owners drink a certain beverage, smoke a certain brand of cigar and keep a certain pet.
• No owners have the same pet, smoke the same brand of cigar or drink the same drink.
• Hints:
  • The Brit lives in a red house.
  • The Swede keeps dogs as pets.
  • The Dane drinks tea.
  • The green house is on the left of the white house.
  • The green house owner drinks coffee.
  • The person who smokes Pall Mall rears birds.
  • The owner of the yellow house smokes Dunhill.
  • The man living in the house right in the centre drinks milk.
  • The Norwegian lives in the first house.
  • The man who smokes Blend lives next to the one who keeps cats.
  • The man who keeps horses lives next to the man who smokes Dunhill.
  • The owner who smokes Blue Master drinks beer.
  • The German smokes Prince.
  • The Norwegian lives next to the blue house.
  • The man who smokes Blend has a neighbor who drinks water.

Question:

Can you determine who keeps fish?

Answer

The code calculates possible combinations based on hints.

+ Show code- Hide code library(OpasnetUtils) library(reshape2) library(ggplot2) a <- tidy(opbase.data("Op_en5701.facts")) # List of possible values. e <- tidy(opbase.data("Op_en5701")) # List of known relations between possible values. a <- a[ , colnames(a) != "Obs"] e <- e[ , colnames(e) != "Obs"] # Create all possibilities b <- a[1] for(i in 2:ncol(a)) { b <- merge(b, a[i]) } b <- data.frame(Row = 1:nrow(b), b) b <- melt(b, id.vars = "Row") d <- b # Eliminate all possibilities that are not according to hints. for(i in 1:nrow(e)) { cond <- as.character(e[i, 1]) temp <- merge( b[b$value != cond & b$variable == b[b$value == cond, "variable"][1], ], b[b$value == as.character(e[i, 2]), ], by = "Row" ) d <- d[!d$Row %in% temp$Row, ] cond <- as.character(e[i, 2]) temp <- merge( b[b$value == as.character(e[i, 1]), ], b[b$value != cond & b$variable == b[b$value == cond, "variable"][1], ], by = "Row" ) d <- d[!d$Row %in% temp$Row, ] } d <- reshape(d, idvar = "Row", v.names = "value", timevar = "variable", direction = "wide") colnames(d) <- gsub("value.", "", colnames(d)) cat("The remaining possibilities based on the given data:\n") oprint(d) ggplot(d, aes(Nationality, weight=1, fill=Pet)) + geom_bar(position="dodge") + scale_x_discrete("Nationality") + scale_y_continuous("Frequency")

These cannot be solved with this solver:

• The green house is on the left of the white house.
• The man who smokes Blend lives next to the one who keeps cats.
• The man who keeps horses lives next to the man who smokes Dunhill.
• The Norwegian lives next to the blue house.
• The man who smokes Blend has a neighbor who drinks water.

Rationale

Possible values of different properties. The different columns are NOT related, i.e. this is just an exhaustive list of possibilities without any information about which things belong together.

facts(-)

Obs	House number	House colour	Nationality	Pet	Drink	Tobacco
1	House 1	Red house	Brit	Dog	Tea	Pall Mall
2	House 2	Green house	Swede	Bird	Coffee	Dunhill
3	House 3	Yellow house	Dane	Cat	Milk	Prince
4	House 4	White house	Norwegian	Horse	Beer	Blend
5	House 5	Blue house	German	Fish	Water	Blue Master

The known relations as a table.

Einstein quiz(-)

Obs	First	Second
1	Brit	Red house
2	Swede	Dog
3	Dane	Tea
4	Green house	Coffee
5	Pall Mall	Bird
6	Yellow house	Dunhill
7	House 3	Milk
8	Norwegian	House 1
9	Blue Master	Beer
10	German	Prince

See also

• The real solution to Einstein quiz

Related files

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