Problem 17 · 2021 Math Kangaroo
Medium
Logic & Word Problems
casework
Ronja had four white tokens and Wanja had four grey tokens. They played a game in which they took turns to place one of their tokens to create two piles. Ronja placed her first token first. Which pair of piles could they not create?
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Answer: E
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Hint 1 of 2
Tokens are placed alternately starting with a white one, so the placing order constrains each pile.
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Hint 2 of 2
Reconstruct the colour pattern each option needs and find the one no legal alternating order can produce.
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Approach: test each stacking against the alternating rule
- Ronja (white) places first, then they alternate colours as they build the two piles.
- For each option, try to order the eight placements so colours alternate and the piles end up as shown.
- Only the pair in choice E cannot arise from any valid alternating sequence.
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