Example Question

[Back to the Logic Puzzle]

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.