Logical Puzzles

What you need to understand

Each person has exactly one item and each item belongs to exactly one person.

A clue naming a person and an item settles that pair immediately.

A clue saying someone does not have something removes one possibility for that person.

A clue saying someone has neither of two things removes two possibilities at once.

When a person is left with a single possible item, that pair is settled.

When an item is left with a single possible owner, that pair is settled just as firmly.

Work outwards from the settled pairs, because each one removes a possibility from everybody else.

How to work through these questions

Draw a grid of people against items, and cross out a pair wherever a clue rules it out.

Fill in the pairs the clues settle outright.

After each settled pair, cross that item off for everyone else and that person off for every other item.

Look for a row or a column with only one possibility left and settle it.

Repeat until nothing more can be settled.

Check the finished arrangement against every clue, not only the ones you used.

Mistakes that cost marks

Forgetting that a settled item cannot belong to anyone else, which is what drives the elimination.
Reading a clue that rules a pair out as though it settled a pair.
Missing that a neither clue rules out two items at once.
Stopping when the answer looks likely rather than when the clues force it.
Answering which item a person has when the question asked who has a given item.
Ignoring a clue because it seemed unhelpful, when it is the one that closes the puzzle.

Worked example

Four friends each have a different pet. Bela has the fish. Divya has the dog. Chetan has neither the fish nor the bird. Who has the dog?

Bela has the fish and Divya has the dog, so those two pairs are settled.
That leaves Chetan and Arun, and the pets still unplaced are the cat and the bird.
Chetan has neither the fish nor the bird, so of the two remaining pets Chetan must have the cat.
Arun therefore has the bird, and every friend has a different pet as required.
The question asks who has the dog, and the clues settle that Divya does.

Answer: Divya

Practice questions with answers

A few Logical Puzzles questions with the full solution shown, so you can see how the method is applied before you attempt the timed set.

Question 1

Four friends Arun, Bela, Chetan and Divya each have a different pet.
(1) Bela has neither the cat nor the bird.
(2) Chetan has neither the fish nor the bird.
(3) Divya has neither the dog nor the fish.
(4) Bela has the dog.
Who has the dog?

A Divya
B Chetan
C Arun
D Bela

Answer: Option D — with explanation

Only one arrangement gives every friend a different pet and satisfies all 4 clues, and in it Bela has the dog. Common mistakes - read one of the clues as naming the person it rules out: Divya - read one of the clues as naming the person it rules out: Chetan - read one of the clues as naming the person it rules out: Arun

Question 2

Four friends Arun, Bela, Chetan and Divya each have a different pet.
(1) Divya has neither the dog nor the bird.
(2) Chetan does not have the dog.
(3) Divya has the cat.
(4) Bela has the fish.
Which pet does Arun have?

A cat
B dog
C bird
D fish

Answer: Option B — with explanation

Only one arrangement gives every friend a different pet and satisfies all 4 clues, and in it Arun has the dog. Common mistakes - read one of the clues as naming the person it rules out: fish - read one of the clues as naming the person it rules out: bird - read one of the clues as naming the person it rules out: cat

Question 3

Four friends Arun, Bela, Chetan and Divya each have a different colour.
(1) Divya has neither the red nor the green.
(2) Arun has the blue.
(3) Bela has neither the green nor the yellow.
Who has the yellow?

A Arun
B Bela
C Divya
D Chetan

Answer: Option C — with explanation

Only one arrangement gives every friend a different colour and satisfies all 3 clues, and in it Divya has the yellow. Common mistakes - read one of the clues as naming the person it rules out: Arun - read one of the clues as naming the person it rules out: Chetan - read one of the clues as naming the person it rules out: Bela

Question 4

Four friends Arun, Bela, Chetan and Divya each have a different colour.
(1) Chetan has the yellow.
(2) Arun has neither the blue nor the yellow.
(3) Bela has the green.
(4) Bela does not have the red.
Which colour does Bela have?

A red
B green
C yellow
D blue

Answer: Option B — with explanation

Only one arrangement gives every friend a different colour and satisfies all 4 clues, and in it Bela has the green. Common mistakes - read one of the clues as naming the person it rules out: yellow - read one of the clues as naming the person it rules out: red - read one of the clues as naming the person it rules out: blue

Question 5

Four friends Arun, Bela, Chetan and Divya each have a different sport.
(1) Chetan has neither the tennis nor the chess.
(2) Divya has the cricket.
(3) Bela does not have the hockey.
(4) Arun has the chess.
Who has the tennis?

A Bela
B Arun
C Chetan
D Divya

Answer: Option A — with explanation

Only one arrangement gives every friend a different sport and satisfies all 4 clues, and in it Bela has the tennis. Common mistakes - read one of the clues as naming the person it rules out: Arun - read one of the clues as naming the person it rules out: Chetan - read one of the clues as naming the person it rules out: Divya

Frequently asked questions

Do I need to work out the whole arrangement?

Not always, but it is usually quicker than reasoning about one answer in isolation. The same elimination that settles the other friends settles the question.

What does a clue saying someone has neither of two things tell me?

It rules out two items for that person at once, which is often enough to settle them when only two were possible.

How should I lay out the work?

Draw a grid of people against items, cross out what each clue rules out, and fill in a pair only when its row or column has a single possibility left.

Can two people have the same pet?

No. Every friend has a different pet, and that is what lets the puzzle be solved by elimination rather than by choice.

What if a clue seems to rule everything out?

Then an earlier step was misread. Return to the clue you used last and check whether it settled a pair or merely ruled one out.