IMC 2004 Q2
2. 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?
- A 2
- B 3
- C 4
- D 5
- E 6
Intermediate Mathematical Challenge 2004, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 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.
Solution © UK Mathematics Trust, from the IMC 2004 solutions.