Analysis of Five houses - Mystery Master

Mystery Master

Analysis of Five houses

Michael Benson


This two-star logic puzzle has 6 noun types, 5 nouns per type, 3 links, 14 facts, and no rules. It needs 375 marks and 15 grids. This puzzle is a "healthy" version of a puzzle some attribute to either Albert Einstein or Lewis Carroll. What's interesting about this puzzle is that each clue represents exactly one fact. The six noun types are: House, Color, Nationality, Hobby, Pet, and Drink. Note that my preference is to not pluralize the names for the noun types.

For this analysis, let's try to solve this puzzle with incremental help from the program. Please select the Setup tab, and uncheck All for the Finder. This means the program will not find any marks via the Finder class. Since we do want some help, let's check All for the Lawyer, but uncheck all laws except Law 1. If you are unfamiliar with the laws, please read the help article on the laws.

Law 1

Law 1, the fundamental law of logic grid puzzles, will fill the corresponding row and column in a subgrid with 'X' characters whenever an 'O' character is entered.

Facts of Type 1

Facts that have the link "with" are called type 1 facts. These facts are given below. To learn more about the different types of facts, please read the help article on facts.

  1. The Englishman lives in the red house.
  2. The Spaniard owns dogs.
  3. Coffee is drunk in the green house.
  4. The Ukrainian drinks tea.
  5. The stamp collector owns snails.
  6. The antiques collector lives in the yellow house.
  7. The man in the middle house drinks milk.
  8. The Norwegian lives in the first house.
  9. The man who gardens drinks juice.
  10. The Japanese man's hobby is cooking.

These ten facts all have a positive verb, so please select the Grids tab, and enter 'O' in the appropriate ten cells. Thanks to Law 1, each time you enter 'O', the program fills in the subgrid with the necessary 'X' characters. When you are done, you should have a total of 90 marks. This is well short of the 375 total marks we need.

The facts that we still need to examine are given below. These facts reference the relationships "directly to the right of", and "next to". In Mystery Master parlance, a relationship consists of a verb and a link, so these three facts all have the implicit verb "is", and what I just called a relationship is really a link. I hope the fog that just formed in your brain eventually clears.

  1. The green house is directly to the right of the white one.
  2. The man who sings lives next to the man with the fox.
  3. The antiques collector lives next to the man with the horse.
  4. The Norwegian lives next to the blue house.


The beginning of this puzzle stated that five houses are in a row. The easiest way to think of this is to label the first house as "1st", the house to its right as "2nd", and so on. Here is how this looks in case you're still suffering from "foggy brain".


Each link in a puzzle must be based on a noun type. All three links in this puzzle use the noun type House. Please make sure you understand the links given in the Links tab before you continue.

Facts of Type 2

Facts of type 2 involve a noun of the link's noun type. If fact 8 was restated as "The man who drinks milk is directly to the right of the 2nd house.", this would be a fact of type 2. But as it is, none of the facts are of type 2.

Facts of Type 3

A fact where both nouns have the same noun type are type 3 facts. Fact 5 is in this category.

Facts of Type 4

A fact where both nouns have different noun types are type 4 facts. Facts 10, 12, and 14 are in this category. The subtle difference between facts of type 3 and 4 is this: The two nouns in a type 4 fact may be together.

Just the Facts

If we examine fact 5, "The green house is directly to the right of the white one.", we should take a peek at the subgrid for House and Color. Though currently empty, is there anything we can enter for this fact? Mull this over before continuing.

Okay, enough mulling. The green house cannot be 1st, just as the white one cannot be 5th. We have 92 marks.

If we examine fact 10, there's one obvious reveal: "The man who sings does not own the fox." We have 93 marks.

If we examine fact 12, there's one obvious reveal: "The antiques collector does not own the horse." We have 94 marks.

If we examine fact 14, there's one obvious reveal: "The Norwegian does not live in the blue house." We have 95 marks.

Examining fact 14 further, if the Norwegian lives in the first house (clue 9), then the blue house must be the second house! We now have 104/375 marks and 11/75 pairs.

If Level 1 was enabled, along with Law 1, the Mystery Master program would also find the same 104 marks. So what should we do? The answer is obvious; we need more laws!

Law 2

If we enable Level 1 along with Laws 1 and 2, the program can find 139/375 marks, but we still have only 11/75 pairs. What did Law 2 do? It combined mark 2 (The Spaniard is not in the red house) with mark 10 (The Spaniard owns dogs) to give us mark 19: "The dogs are not in the red house."

Law 2 is responsible for 36 marks, so one of the marks could have been found with just Law 1 enabled.

Law 3

If we enable Level 1 along with Laws 1 - 3, the program can find 143/375 marks, but again we still have only 11/75 pairs. What did Law 3 do? For mark 127, it determined that the owner of the green house and the one who collected stamps could not be the same person. Why? Because they do not have a nationality in common. After mark 126, the owner of the green house could be the Spaniard or the Japanese, while the one who collected stamps was either the Englishman, the Ukranium, or the Norwegian.

Law 3 is responsible for 4 marks.

Law 4

If we enable Level 1 along with Laws 1 - 4, the program does not find any additional marks.

Law 5

If we enable Level 1 along with all of the laws, the program can find the solution. Law 5 is first invoked to enter mark 75. It combines mark 73 (The third house is not green.) with fact 5 (The green house is directly to the right of the white one.) to give us mark 75: "The second house is not white."

Though Law 5 is only invoked 14 times, it allows all of the laws to enter 365/375 marks, and 65/75 pairs.


This analysis tried to show you how versatile the Mystery Master program can be. It also showed you how powerful the Laws are when it comes to solving a logic puzzle.