Problem 9 · 2022 Math Kangaroo
Medium
Logic & Word Problems
work-backwardcareful-counting
Five cars are labelled 1 to 5 and drive in the direction of the arrow. First the last car overtakes the two cars in front of it. Then the car that is now second to last overtakes the two in front of it. Finally the car that is now in the middle overtakes the two in front of it. In what order do the cars drive now?
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Answer: B — 2, 1, 3, 5, 4
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Hint 1 of 3
Write the five car numbers in a row (front car first) and act out the story move by move.
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Hint 2 of 3
When a car overtakes the two in front of it, slide it forward so it sits just ahead of both of those two cars.
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Hint 3 of 3
Do the three moves one at a time and read off the new order at the end.
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Approach: act out the overtakes one move at a time
- The arrow points left, so the front-to-back order starts as 1, 2, 3, 4, 5 (car 1 leads).
- The last car (5) jumps past the two in front of it (4 and 3): now 1, 2, 5, 3, 4.
- The new second-to-last car (3) jumps past the two in front of it (5 and 2): now 1, 3, 2, 5, 4.
- The car now in the middle (2) jumps past the two in front of it (3 and 1): now 2, 1, 3, 5, 4 — answer B.
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