Perfect Score

Can you work out how many children answered all the questions correctly?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



100 children took part in a Mathematics competition consisting of four problems.

90 children solved the first problem

85 solved the second

80 solved the third

75 solved the last problem

What is the minimum number of children who could have answered all the questions correctly?

This problem is taken from the UKMT Mathematical Challenges.