Problem 2 · 2011 Math Kangaroo
Easy
Logic & Word Problems
casework
Three racers take part in a Formula-1 race: Michael, Fernando and Sebastian. At the start Michael leads, ahead of Fernando, who is ahead of Sebastian. During the race Michael and Fernando overtake each other 9 times, Fernando and Sebastian 10 times, and Michael and Sebastian 11 times. In what order do the three finish?
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Answer: B — Fernando, Sebastian, Michael
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Hint 1 of 2
Two racers swap order exactly once each time they overtake one another, so only the parity of each count matters.
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Hint 2 of 2
Odd number of swaps reverses a pair's order; even keeps it the same.
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Approach: track each pair's order by the parity of its overtakes
- Start: Michael, Fernando, Sebastian.
- Michael–Fernando: 9 swaps (odd) → Fernando now ahead of Michael.
- Fernando–Sebastian: 10 (even) → Fernando stays ahead of Sebastian.
- Michael–Sebastian: 11 (odd) → Sebastian now ahead of Michael.
- So Fernando > Sebastian > Michael: order Fernando, Sebastian, Michael.
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