Problem 17 · 2011 Math Kangaroo
Hard
Logic & Word Problems
work-backward
Four friends Masha, Sasha, Dasha and Pasha are sitting on a bench. At first Masha swapped places with Dasha. Then Dasha swapped places with Pasha. After this the four friends are sitting from left to right in the order: Masha, Sasha, Dasha, Pasha. In what order, from left to right, were they sitting to begin with?
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Answer: C — Dasha, Sasha, Pasha, Masha
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Hint 1 of 2
Undo the swaps in reverse order, starting from the final seating.
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Hint 2 of 2
First undo the Dasha–Pasha swap, then the Masha–Dasha swap.
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Approach: reverse the swaps
- Final order: Masha, Sasha, Dasha, Pasha. Undo the last swap (Dasha↔Pasha): Masha, Sasha, Pasha, Dasha.
- Undo the first swap (Masha↔Dasha): the start was Dasha, Sasha, Pasha, Masha, answer C.
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