Birthday party
The 30 students in a class have 25 different birthdays between them. What is the largest number that can share any birthday?
Age
11 to 14
Challenge level
Problem
You are told that 30 pupils have 25 different birthdays between them. What is the largest number of these pupils who could share the same birthday?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: 6
There must be 25 pupils who all have different birthdays. If the remaining 5 pupils all have the same birthday as one of these pupils, then 6 pupils will share the same birthday.
There must be 25 pupils who all have different birthdays. If the remaining 5 pupils all have the same birthday as one of these pupils, then 6 pupils will share the same birthday.