Problem 23 · 2017 Math Kangaroo
Stretch
Arithmetic & Operations
careful-countingtotal-then-divide
Kate has four flowers, which have 6, 7, 8 and 11 petals respectively. She now tears off one petal from each of three different flowers. She repeats this until it is no longer possible to tear off one petal from each of three different flowers. What is the minimum number of petals left over?
Show answer
Answer: B — 2
Show hints
Hint 1 of 2
Every single round takes away exactly 3 petals (one from each of three flowers).
Still stuck? Show hint 2 →
Hint 2 of 2
Since 3 petals leave each round, the petals removed always count up by threes; think about what is left from 32.
Show solution
Approach: petals leave 3 at a time, so the leftover is what 32 has past a count-by-three
- There are 6 + 7 + 8 + 11 = 32 petals to start.
- Each round takes one petal from three different flowers, so exactly 3 petals leave every round.
- Counting by threes (3, 6, 9, ..., 30), the most she can remove is 30, which still keeps three flowers alive long enough to do every round.
- That leaves 32 - 30 = 2 petals.
Mark:
· log in to save