Problem 18 · 2020 Math Kangaroo
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Logic & Word Problems
careful-countingoff-by-one
Two equal trains, each with 31 numbered wagons, travel in opposite directions. When wagon number 7 of one train is side by side with wagon number 12 of the other train, which wagon is side by side with wagon number 11?
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Answer: A — 8
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Hint 1 of 2
The two trains line up wagon-to-wagon; use the spot where 7 meets 12.
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Hint 2 of 2
The two facing wagon numbers always add up to the same total.
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Approach: pair wagons from the known matching point
- Wagon 7 of one train lines up with wagon 12 of the other.
- The wagon numbers run in opposite directions, so the two numbers across from each other always add to 19 (that is 7 plus 12).
- Across from wagon 11 is the wagon numbered 19 minus 11 = 8.
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