Who Owns the Fish Reasoning Puzzle: Third Solution

The puzzle has 15 hints and asks—Who owns the fish? Hints on how five persons in 5 styled houses own pets, drinks coffee and travel. Learn reasoning.

Who Owns the Fish Reasoning Puzzle Similar to Einstein's Puzzle

Hints:

1. Nicola lives in the tartan house.
2. Ed has a guinea pig.
3. David drinks mochaccino.
4. The paisley house is on the left of the gingham house.
5. The owner of the paisley house drinks flat whites.
6. The person who drives by car has a squirrel.
7. The owner of the striped house travels by bike.
8. The person living in the center house drinks double espresso.
9. Nick lives in the first house.
10. The person who travels by train lives next to the one who has a pitbull.
11. The person who has a badger lives next to the person who travels by bike.
12. The person who travels by plane drinks chai latte.
13. Nigel goes everywhere by foot.
14. Nick lives next to the polka dot house.
15. The person who travels by train has a neighbor who drinks decaf.

Who owns the fish?

Time for you to find the answer is 30 minutes.

Hints for solving:

• Identify the primary object, its properties and the property values.
• Select the hints that create direct assignment of property values to their rightful house positions (not occupants).
• To keep track of the assignments obtained, use a table of 5 columns (with house positions as headers) and of 5 rows, each for one property.
• Identify relations between property values and use for breakthroughs.
• Solve taking no extra steps.

Don't read more before solving (or failing to solve) the puzzle.

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Solution to Who Owns the Fish Reasoning Puzzle Similar to Einstein's Puzzle: Preparation

Identify Objects, Properties of Objects and their Values

• Identify the primary object: A house—identified by its position. Five houses are in positions 1, 2, 3, 4 and 5. House 1 is the FIRST, and House 3 is at the CENTER.
• Identify the properties of the primary object and its values: Directly related single property is house style:
• Style property values: tartan, striped, paisley, polka dot, and gingham.
• Identify the secondary object as a property of a house and its values: An occupant of a house:
• Occupant: Nick, Ed, David, Nicola, and Nigel.
• Identify the other properties and values of the properties:
• Pet: guinea pig, pitbull, badger, squirrel and the fish (not mentioned in any hint).
• Drinks coffee: mochaccino, flat whites, double espresso, chai latte, and decaf.
• Travel mode: car, train, plane, bike, and foot.
• Ownership: A house in a specific position will own a value of a specific property when found out so by the hints.
• Transitive ownership: As a house owns the occupant living in it, his pet, coffee drinking type and travel mode will automatically be owned by the house.

Method to record and track property value ownerships

• To simplify, five houses will be positioned from left to right in position 1, 2, 3, 4 and 5.
• A property value, such as, an occupant living in a house will be assigned the position under that house column, and in the row of "Occupant" property.
• Natural form of noting and keeping track of ownerships is a five row by five column table.
• The column headers are House 1, House 2, House 3, House 4 and House 5. The row labels are the property names.
• Finding an ownership of a property value is technically known as an assignment. The assignments to be noted in the 5x5=25 cell assignment table.
• Each breakthrough in finding an ownership of a property value will be noted in the cell intersecting the property row and the house column.
• At the start, all the cells will be vacant, as no property value ownership is known in the beginning.

Advantages of noting and tracking assignments:

• It helps to identify the more promising row with many cells filled up at any stage.
• Together with the state of the assignment table and analysis of the hints, the next steps to take are decided.

Understand the nature of the hint statements

Before taking any decisive step, it is essential to make a quick scan analysis of the hint statements searching for hints:

• That fix a property value to a house position—a direct assignment.
• That relate any two (or more) values of the same property in a fixed way of occupying house positions—a horizontal bond—most valuable advanced form of help for breakthrough assignments.
• That relate two (or more) values of separate properties of the same owner—a vertical bond—valuable in getting breakthrough by conflict or creating a more powerful pattern—a Cell block.

A quick scan reveals a few direct assignment hints, one horizontal bond and many vertical bonds.

Goal: To assign most property values at the earliest, revealing the elusive owner of the fish automatically.

This type of reasoning puzzles are also known as Grid puzzles (because of 5 by 5 grid of cells in this case) or Assignment puzzles.

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Solution to Who Owns the Fish Reasoning Puzzle Similar to Einstein's Puzzle: Assignments by Hint Analysis

Stage 1: Direct assignments first and Assignment by Link search technique

Scan all the hints to identify:

• Hint 9: Nick lives in the first house.
• ⇨ Nick assigned to House 1 as the "Occupant".

Also,

• Hint 8: The person living in the center house drinks double espresso.
• ⇨ "double espresso" as the "Coffee" assigned to the House 3—occupant drinks—transitive assignment (though owner is unknown now).
• Hint 14: Nick lives next to the polka dot house.
• ⇨ With Nick in House 1, the "Style" of House 2 gets "polka dot".
• Always look for this type of additional assignments by linked reference.

The assignment table after the first stage of simple assignments.

Stage 2: Advanced techniques: Use a Horizontal Bond and a Vertical Bond for an Assignment by Default

Logical reasoning:

• Hint 4: "The paisley house is on the left of the gingham house": a positional relation between two values of the same property—a horizontal bond.
• Result: The first two positions are eliminated from the positions the "paisley-gingham" Style pair can occupy, leaving position 3, 4 and 5 for the pair.
• Hint 1: "Nicola lives in the tartan house": two property values of the same position are related—a vertical bond.
• Result: With the "Style" and "Occupant" conflicting, the vertical bond "Nicola-tartan" cannot also occupy the first two positions.
• Breakthrough: The positions 3, 4 and 5 must be occupied by the three "Style" values: "paisley", "tartan" and "gingham". The fifth "Style" value "striped" gets position 1 by default.

Use link search:

• Hint 7: "The owner of the striped house travels by bike."
• Hint 11: "The person who has a badger lives next to the person who travels by bike."
• Result: "Travel mode" value of "bike" assgned to position 1 and "Pet" value "badger" to position 2.

Resolve position of "Style" value "paisley" by the horizontal bond and "Coffee" conflict:

• Hint 4: "The paisley house is on the left of the gingham house": "paisley" can occupy either position 3 or 4.
• Hint 5: "The owner of the paisley house drinks flat whites": The "Coffee" value "flat whites" of "paisley" house owner eliminates position 3 (who drinks "double espresso").
• Results: "paisley-gingham" assigned to positions 4 and 5 for "Style" and "flat whites" to position 4 as the "Coffee".

The position 3 for "Style" gets "tartan" by default and link search on "tartan":

• Hint 1: "Nicola lives in the tartan house": "tartan" and "Nicola" assigned to position 3.

This much for stage 2. The assignment table:

Stage 3: Critical breakthrough by conflicts in the most occupied row with a pair of hints taken together

"Coffee" being the most occupied property row, we will resolve the position of "decaf" referred by only the hint 15:

• Hint 15: "The person who travels by train has a neighbor who drinks decaf."
• Result: "decaf" can occupy positions 1, 2 or 5.

The other two values of "Coffee" referred by two separate hints 3 and 12:

• Hint 3: "David drinks mochaccino": "mochaccino" can occupy positions 2 or 5.
• Hint 12: "The person who travels by plane drinks chai latte": "chai latte" can also occupy positions 2 or 5.
• Result: No hints except hint 15 claims position 1 for "decaf".

The intermediate stage of the assignment table showing the claims of positions by "Coffee" values by the three hints 3, 12 and 15 and no other:

The position 1 has no claims for any "Coffee" values other than "decaf".

Critical breakthrough: By general problem solving No-takers technique, "decaf" assigned to position 1 which has no claim for it other than "decaf".

Supporting logical reasoning for breakthrough assignments:

• If "decaf" occupies either of positions 2 or 5, one of "mochaccino" and "chai latte" won't have any valid position.
• Conclusion: "decaf" can occupy only position 1.
• Hint 15: "The person who travels by train has a neighbor who drinks decaf": "Travel mode" value "train" gets position 2.

The assignment table showing the critical breakthrough at the stage 3.

Stage 4: Critical breakthrough removes any more hurdles to the solution by simple assignments

First assignment: "plane-chai latte" has only viable position 5.

• Hint 12: "The person who travels by plane drinks chai latte": The vertical bond "chai latte-plane" assigned to position 5 and the fifth "Coffee" value "mochaccino" has only the position 2.

Link search:

• Hint 3: "David drinks mochaccino": "mochaccino-David" can occupy only positions 2.

Next, for the vertical bond "Nigel-foot" in Hint 13 the only position available is 4.

• Hint 13: "Nigel goes everywhere by foot": "Nigel-foot" in position 4, the fifth value "Ed" becomes the occupant of House 5 by default, and the fifth value "car" is the "Travel mode" for the occupant of House 3 by default.

Link search for "Ed" and "car":

• Hint 2: "Ed has a guinea pig": "guinea pig" is the Pet for Ed in House 5.
• Hint 6: "The person who drives by car has a squirrel": The pet of the owner of the third house is "squirrel".

With "squirrel" occupying position 3, the only neighbor of the person traveling by train lives in House 1:

• Hint 10: "The person who travels by train lives next to the one who has a pitbull": The occupant of House 1 has the Pet "pitbull" and the fifth Pet value "fish" must be in the only available position 4 by default.

Ultimate assignment table:

The pet "fish" kept by the occupant "Nigel" living in House 4.

Answer: Nigel owns the fish.

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Summing up

This reasoning puzzle is the same as the famous and most popular Einstein's puzzle with all names changed.

• In my last masterclass foundation article for reasoning puzzles, I have shown two ways to solve the puzzle.
• Here, I have showed how this timeless reasoning puzzle can be solved in following a third path of using the novel general problem solving No-takers technique and logical reasoning.

The foundation laid down in the first solution should get a good additional strength from this third solution.

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More puzzles to enjoy

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You may also look at the full collection of puzzles at one place in the Challenging brain teasers with solutions: Long list.

Enjoy puzzle solving while learning problem solving techniques.

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