Problem 10 · 2017 Math Kangaroo
Hard
Counting & Probability
Logic & Word Problems
careful-counting
A whimsical teacher has a box with 203 red, 117 white and 28 blue buttons. He asks his students to each take one button out of the box without looking. What is the minimum number of students who have to take a button so that definitely at least three of the buttons picked have the same colour?
Show answer
Answer: C — 7
Show hints
Hint 1 of 2
Think about the worst possible luck before three match.
Still stuck? Show hint 2 →
Hint 2 of 2
There are only three colours, so how many can you draw with at most two of each?
Show solution
Approach: pigeonhole: build the worst case, then add one
- In the worst case each colour comes up at most twice: 2 + 2 + 2 = 6 buttons with no colour reaching three.
- The very next button (the 7th) must repeat some colour for a third time.
- So 7 students guarantee three of one colour, choice C.
Mark:
· log in to save