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 known relations as a table.

Einstein quiz: Difference between revisions(-)

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

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.

+ Show code- Hide code library(reshape) library(ggplot2) a <- data.frame(A = c("A", "B", "C", "D", "E"), B = c("a", "b", "c", "d", "e"), C = c("1", "2", "3", "4", "5")) e <- data.frame(F = c("A", "a", 1), S = c("b", "2", "D")) cat("Initiation successful. Now starting model.\n") a <- fetch("Op_en5700") # List of possible values. e <- fetch("Op_en5701") # List of known relations between possible values. 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 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") print(xtable(d), type = 'html', html.table.attributes = "class='sortable'") ggplot(d, aes(Nationality, weight=1, fill=Pet)) + geom_bar(position="dodge") + scale_x_discrete("Nationality") + scale_y_continuous("Frequency")

See also

• The real solution to Einstein quiz

Related files

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