Problem 1 · 2017 Math Kangaroo
Easy
Logic & Word Problems
casework
Four cards are placed in this order (see picture). Which order shown in the options cannot be obtained if only two cards are swapped?
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Answer: B
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Hint 1 of 2
A single swap exchanges exactly two of the four cards and leaves the other two where they are.
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Hint 2 of 2
Check each option: can you reach it from 2 0 1 7 by moving just two cards? One option needs three cards to shift.
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Approach: test each ordering against the one-swap rule
- Starting order is 2 0 1 7. A swap trades the positions of exactly two cards.
- 2 7 1 0 swaps the 0 and the 7; 1 0 2 7 swaps the 2 and the 1; 0 2 1 7 swaps the 2 and the 0; 2 0 7 1 swaps the 1 and the 7 — all reachable.
- To turn 2 0 1 7 into 0 1 2 7 the 2, 0 and 1 must all move (a three-card cycle), which one swap cannot do.
- So 0 1 2 7 (B) is impossible.
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