Logic Puzzles
Joe Wolfensohn
Teacher
Introduction - Logic Puzzles
What is a Logic puzzle?
In the exam, you will be presented with a short scenario usually in the form of a short paragraph of text describing the situation, a list of rules or a simple diagram.
Using the given information, you must deduce or infer a correct conclusion using the information.
Example
Three friends Amir, Ben, and Cara each have a different favourite fruit: apple, banana, or cherry.
You are given the following information:
1. Amir does not like bananas.
2. The person who likes cherries is not Ben.
3. Cara does not like apples.
Who likes bananas?
Why are logic puzzles used in the UCAT?
Tests your ability to draw conclusions based on rules and assumptions.
Helps you to develop deductive reasoning and making decisions based on available information.
Working methodically in applying logic step-by-step under time pressure.
Worked Examples
Question 1 - Easy
Four people A, B, C, and D are a chef, an artist, a scientist, and an engineer, not necessarily in that order. They each own a different kind of pet.
A is an artist.
B owns a parrot.
D owns a goldfish.
The person who owns a cat is not the engineer.
The chef takes her dog on a walk every evening.
Which one of the following MUST be true?
A. D is a chef.
B. C owns a cat.
C. B is a scientist.
D. A is not the engineer.
Answer
D. A is not the engineer.
Worked Solution
When answering these questions, it is essential that we draw a table or a diagram to represent the information given, to save time. Write the first letter(s) of each ‘category’ when filling in the table to save time.
E.g.
CH = chef AR = artist SC = scientist ENG = Engineer
P = parrot G = goldfish Ca = Cat
| CH | AR | SC | ENG | Pet | |
| A | |||||
| B | |||||
| C | |||||
| D |
In the table above, we have the occupations across the top, and the four people (A, B, C and D) going down.
We can now fill in our table using the information given:
- A is an artist.
- B owns a parrot.
- D owns a goldfish.
| CH | AR | SC | ENG | Pet | |
| A | ✓ | ||||
| B | Parrot | ||||
| C | |||||
| D | Goldfish |
Using the information given, we can also draw conclusions to fill in the table:
- ‘The chef takes her dog on a walk every evening.
From this information, we can conclude that the chef owns a pet dog. The only row in the table where the occupation and pet is not filled in is person C.
Therefore, we can conclude that C is a chef and owns a pet dog.
| CH | AR | SC | ENG | Pet | |
| A | ✓ | ||||
| B | Parrot | ||||
| C | ✓ | Dog | |||
| D | Goldfish |
As there is only one gap in the ‘Pet’ column, we can conclude that person A owns a cat.
| CH | AR | SC | ENG | Pet | |
| A | ✓ | Cat | |||
| B | Parrot | ||||
| C | ✓ | Dog | |||
| D | Goldfish |
Looking at the answer options, the only option that can be true is D - A is not the engineer. This is because we have already concluded that A is an artist based on the information given.
Question 2 - Medium
Five students - Alice, Ben, Charlie, Diana, and Ethan each borrowed a book and pen which were different colours: red, orange, green, blue and purple.
No student borrowed a book and pen that were the same colour.
Diana borrowed an orange book. Her pen was neither red nor blue.
Ethan borrowed a blue book.
Ben borrowed a green pen. The colour of his book was the same colour as Diana’s pen.
Which of the following statements is true?
A. Charlie borrowed a purple book.
B. Ethan borrowed a purple pen.
C. Ethan borrowed a blue pen.
D. Alice borrowed a red or green book.
Answer
D. Alice borrowed a red or green book.
Worked Solution
Draw diagrams/a table to help represent the information given, and write down the list of colours for the books and pens, so you can cross them off as you fill in your table.
- To save time, write the first letter(s) of the different colours e.g. R = red etc.
Book - R, O, G, B and P
Pen - R, O, G B and P
| Book | Pen | |
| Alice | ||
| Ben | ||
| Charlie | ||
| Diana | ||
| Ethan |
0% Chance that Diana’s Pen R/B
Use the information to fill in the table. Crossing of the colours, as we fill in the table.
- ‘Diana borrowed an orange book. Her pen was neither red nor blue.’
- ‘Ethan borrowed a blue book.’
- ‘Ben borrowed a green pen. The colour of his book was the same colour as Diana’s pen.’
Book - R, O, G, B and P
Pen - R, O, G, B and P
| Book | Pen | |
| Alice | ||
| Ben | G | |
| Charlie | ||
| Diana | O | |
| Ethan | B |
0% Chance that Diana’s Pen R/B
Use deduction and logic to fill in the rest of the table:
- We can conclude that Diana’s pen cannot be orange, red or blue. This is because her book cannot be the same colour as her pen (orange) and from the stem it says that her ‘her pen was neither red nor blue’. Therefore, her pen must be purple.
- If Diana’s pen is purple, Ben’s book must be purple because ‘The colour of his book was the same colour as Diana’s pen.’
Book - R, O, G, B and P
Pen - R, O, G, B and P
| Book | Pen | |
| Alice | ||
| Ben | P | G |
| Charlie | ||
| Diana | O | P |
| Ethan | B |
0% Chance that Diana’s Pen R/B
The only colours remaining for books are red or green. We cannot conclude who out of Alice and Charlie borrowed a red or green book. Therefore, we can only conclude that Alice and Charlie borrowed either a red or green book.
Therefore, option D - Alice borrowed a red or green book is correct.
Question 3 - Hard
Four students: Liam, Mia, Noah, and Ava each bake a dessert: a cake, a pie, a brownie, and a cookie. One of the desserts was accidentally burnt in the oven.
Afterwards, they make the following statements:
- Liam says: “It was Mia’s dessert.”
- Mia says: “Noah burnt it.”
- Noah says: “I didn’t do it.”
- Ava says: “I didn’t do it either.”
Only one person is lying.
Which one of the four must be lying?
A. Liam
B. Mia
C. Noah
D. Ava
Answer
B. Mia
Worked Solution
This question type is a bit trickier, as we cannot represent the information in a table. However, we can deduce the answer by working through the question logically.
- Liam’s claim “It was Mia’s dessert.” = false.
- Mia’s “Noah burnt it.” = false.
- Noah “I didn’t do it.” = true.
- va “I didn’t do it either.” = true.
- Result – two liars. Invalid.
- Liam “It was Mia’s dessert.” = true.
- Mia “Noah burnt it.” = false.
- Noah “I didn’t do it.” = true.
- Ava “I didn’t do it either.” = true.
- Result – exactly one liar. Valid.
- Liam “It was Mia’s dessert.” = false.
- Mia “Noah burnt it.” = true.
- Noah “I didn’t do it.” = false.
- Ava “I didn’t do it either.” = true.
- Result – two liars. Invalid.
- Liam “It was Mia’s dessert.” = false.
- Mia “Noah burnt it.” = false.
- Noah “I didn’t do it.” = true.
- Ava “I didn’t do it either.” = false.
- Result – three liars. Invalid.
- Liam is truthful.
- Mia is lying.
- Noah is truthful.
- Ava is truthful.
Worked Examples Video