PK 2017 Q7
7. A certain maths teacher has a box containing buttons of three different colours. There are 203 red buttons, 117 white buttons and 28 blue buttons. A student is blindfolded and takes some buttons from the box at random. How many buttons does the student need to take before he can be sure that he has taken at least 3 buttons of the same colour?
- A 3
- B 4
- C 6
- D 7
- E 28
Pink Kangaroo 2017, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 7
If the student has taken six buttons, he may already have three of the same colour, but it is possible that he has exactly two of each. However, if he takes a seventh button, he is guaranteed to have three of the same colour.
Solution © UK Mathematics Trust, from the PK 2017 solutions.