Problem 14 · 2025 Math Kangaroo
Stretch
Logic & Word Problems
careful-countingcasework
Every time a coin is put into the machine, the bottom ball falls out of one of the five tubes. How many coins does Barbara have to put in to be sure she gets at least one white ball?
Show answer
Answer: D — 11
Show hints
Hint 1 of 3
Imagine Barbara has the unluckiest day — every ball that is not white comes out first.
Still stuck? Show hint 2 →
Hint 2 of 3
Only the bottom ball of a tube can come out, so count the non-white balls that could fall before any white one.
Still stuck? Show hint 3 →
Hint 3 of 3
Add up all those non-white balls, then put in one more coin to be sure of a white ball.
Show solution
Approach: imagine the unluckiest order, then add one more coin
- Each coin drops the bottom ball of some tube, so the worst luck is all the non-white balls coming out first.
- Counting from the bottom of every tube up to its first white ball, 10 non-white balls could fall before any white one.
- After those 10 unlucky balls, the next ball must be white, so she needs 10 + 1 = 11 coins. The answer is D.
Mark:
· log in to save