Problem 18 · 2021 Math Kangaroo
Hard
Logic & Word Problems
work-backward
Every time the witch has 3 apples she turns them into 1 banana. Every time she has 3 bananas she turns them into 1 apple. What will she finish with if she starts with 4 apples and 5 bananas?
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Answer: A
Show hints
Hint 1 of 3
Start with her 4 apples and 5 bananas, and just keep following her two rules.
Still stuck? Show hint 2 →
Hint 2 of 3
Trade 3 apples for 1 banana, and trade 3 bananas for 1 apple, again and again.
Still stuck? Show hint 3 →
Hint 3 of 3
Keep swapping in groups of 3 until you can no longer make a group of three.
Show solution
Approach: repeatedly trade groups of three
- Start with 4 apples and 5 bananas. Trade 3 apples for 1 banana: 1 apple, 6 bananas.
- Trade 6 bananas (two groups of three) for 2 apples: 3 apples, 0 bananas.
- Trade those 3 apples for 1 banana: 0 apples, 1 banana.
- She finishes with a single banana, option A.
Mark:
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