Problem 12 · 2014 Math Kangaroo
Medium
Logic & Word Problems
spatial-reasoning
The kangaroos A, B, C, D and E sit in this order, clockwise, around a round table (see picture). After a bell rings, all but one kangaroo swap seats with a neighbour. Afterwards they sit, clockwise, in the order A, E, B, D, C. Which kangaroo did not change places?
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Answer: B — B
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Hint 1 of 2
Everyone who moved swapped with a next-door neighbour, so the movers come in pairs.
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Hint 2 of 2
Fix the seats and find the one kangaroo whose new neighbours match its old ones — that is the one that stayed put.
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Approach: anchor one seat and check the rest are neighbour swaps
- Before, clockwise: A, B, C, D, E; afterwards, clockwise: A, E, B, D, C.
- Suppose B stays in its seat. Reading the after-order clockwise starting at B gives B, D, C, A, E around the circle.
- Comparing seat by seat with the before arrangement, C and D have simply swapped (they were neighbours) and A and E have swapped (also neighbours), while B never moved.
- Every change is a neighbour swap, so the kangaroo that did not move is B.
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