Unit 1 Section 1 : Logic Puzzles

This section introduces the idea of logic puzzles to help you think mathematically.

Example Question

You have two clues:
Clue 1 : Toni's age is not in the 4-times table.
Clue 2 : Millie's age can be divided exactly by the number of days in a week.

Follow the working below and think about the answers to each of the questions in blue.
When you have worked each answer out, click on the button marked to see whether you were correct.

We can show the information about the sisters and their ages in a logic table:

The logic table can contain three types of symbol: A tick indicates that a particular combination is true. For example, if there was a tick in the centre square, it would mean that Toni was 12 years old. A cross indicates that a particular combination is false. If there was a cross in the bottom-right square, it would mean that Millie was not 14 years old. A question mark appears when no decision has been made yet.

Our first clue is that Toni's age is not in the four times table. What age can Toni not be?

We mark this fact by placing a cross in line with Toni and 12 yrs.

Our second clue is that Millie's age can be divided exactly by the number of days in the week. What age is Millie?

We mark this fact by placing a tick in line with Millie and 14 yrs.

If Millie is 14 yrs old, what other facts about her age can we mark in the diagram?

Can Rana or Toni be 14 years old?

We mark these two extra facts on the diagram as shown: Millie is not 9 years old or 12 years old. Rana and Toni are not 14 yrs old.

Look at Toni's row in the diagram. What age must she be?

We mark a tick in line with Toni and 9 yrs.

If all the girls have different ages, what age must Rana be?

We mark a tick in line with Rana and 12 yrs. We can also mark a cross in the final box because we know that Rana is not 9 years old.

Now we can see that Toni is 9 years old, Rana is 12 years old and Millie is 14 years old.

Exercises

Question 1
Jane, Bill and Kelly each have one pet. They all own different types of pet.

Goldfish Dog Budgie Jane Bill Kelly

Use the logic table and the clues below to find out which pet each person owns. Clue 1 : Kelly's pet does not have a beak. Clue 2 : Bill's pet lives in a bowl.

Question 2
Karen, John and Jenny each play one sport: badminton, tennis or football.

Badminton Tennis Football Karen John Jenny

Use the logic table and the clues below to find out who plays which sport. Clue 1 : John hits a ball with a racket. Clue 2 : Karen kicks a ball.

Question 3
Three children are asked to name their favourite subject out of Maths, P.E. and Art. They each give a different answer.

Maths P.E. Art Daniel Sarah Jane

Use the logic table and the clues below to find out which child chose which subject. Clue 1 : Daniel likes working with numbers. Clue 2 : Sarah does not like to draw or paint.

Question 4
The three children in a family are aged 8, 12 and 16.

8 yrs 12 yrs 16 yrs John Alan Charlie

Use the logic table and the clues below to find the age of each child. Clue 1 : Alan is older than Charlie. Clue 2 : John is younger than Charlie.

Question 5
Amanda, Jo, Alex and Zarah each have different coloured cars.
One car is red, one blue, one white and the other is black.

Red Blue White Black Amanda Jo Alex Zarah

Use the logic table and the clues below to find out which person has which car. Clue 1 : Amanda's car is not red or white. Clue 2 : Jo's car is not blue or white. Clue 3 : Alex's car is not black or blue. Clue 2 : Zarah's car is red.

Question 6
Bill, John, Fred and Jim are married to one of Mrs Brown, Mrs Green, Mrs Black and Mrs White.

Bill John Fred Jim Mrs. Brown Mrs. Green Mrs. Black Mrs. White

Use the logic table and the clues below to decide who is married to who. Clue 1 : Mrs. Brown's husband's name does not begin with J. Clue 2 : Mrs. Black's husband's name has the same letter twice. Clue 3 : The name of Mrs. White's husband has three letters.

Question 7
There are 4 children in a family aged 6, 8, 11 and 14 years old.

6 years 8 years 11 years 14 years Ali Mohammed Dipak Nesima

Use the logic table and the clues below to find the age of each child. Clue 1 : Dipak is three years older than Ali. Clue 2 : Mohammed is older than Dipak.