Problem 9 · 2021 Math Kangaroo
Medium
Logic & Word Problems
careful-countingcasework
Nisa has 3 different types of cards: apple, cherry and grapes. She picks 2 cards from a row and swaps their places. She wants every card showing the same fruit to end up next to each other. For which row is this not possible with a single swap?
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Answer: A
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Hint 1 of 2
A single swap can only move 2 cards, so it can fix a row that is just 2 cards out of place.
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Hint 2 of 2
Check each row: try one swap and see if all the apples, all the cherries, and all the grapes end up touching.
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Approach: test whether one swap can group all like fruits in each option
- One swap picks up just 2 cards and trades their spots, so it can only tidy a row that needs exactly those 2 cards moved.
- Try a single swap on each row and see if it gathers every fruit into one touching group.
- Four of the rows can be sorted with one swap, but in row A no single swap puts all the matching fruits together.
- So the answer is A.
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