Problem 13 · 2018 Math Kangaroo
Stretch
Logic & Word Problems
careful-counting
Alice has 3 white, 2 black and 2 grey pieces of paper. First she cuts every piece of paper that is not black into two pieces. Then she cuts in half every piece of paper that is not white. How many pieces of paper does she have in the end?
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Answer: D — 18
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Hint 1 of 3
Keep three little piles in your head — white, black, and grey — and watch each pile change.
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Hint 2 of 3
Cutting a piece into two means that pile gets twice as many pieces.
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Hint 3 of 3
Do step 1 on the not-black piles, then step 2 on the not-white piles, then add the three piles up.
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Approach: watch each colour pile through the two cuts, then add
- Start with 3 white, 2 black, 2 grey.
- Step 1 cuts every not-black piece in two: white 3 becomes 6, grey 2 becomes 4, and the 2 black stay the same — that is 6 + 2 + 4 = 12 pieces.
- Step 2 cuts every not-white piece in two: black 2 becomes 4, grey 4 becomes 8, and the 6 white stay the same — so 6 + 4 + 8 = 18 pieces.
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