Easter holiday puzzle - Problem solving mathematics

Here is a two-part quiz to puzzle over during the Easter break

Paul and Guy both work at the same company, and car share to get to work. They also enjoy nights out during the week. Because of this they sometimes have a hard start the next morning. One Friday morning, they arrive two hours late, and claim that they had a flat tyre.

Their boss, Gabriel, isn't convinced by their excuse, and asks them to separately write down which tyre was the flat one. They have to do this without communicating with each other.

If they made up the story about the tyres, how likely is it that they will both give the same answer?

On average, Paul and Guy have one night out per month.

How likely is it that this test will allow Gabriel to identify whether they really had a flat tyre?

Did you find the solution difficult or unusual? 

This kind of result is quite normal for practical problem solvers who use maths to help businesses. They do not always have the problem statement clearly defined. To start to develop a solution to a real-world business problem they have to make certain assumptions. These assumptions are then updated as the results are analysed.


With thanks to the Tesco commercial science team