A triathlon consists of three events: swimming, cycling, and running. The contestants are: Adam, Bert, Carl, Doug, and Eric. From the following clues, you must determine: the order of finish in swimming, the order of finish in cycling, the order of finish in running, and the overall rankings.
Points are awarded for each event: 1st place earns 4 points, 2nd earns 3, 3rd earns 2, 4th earns 1, and 5th earns 0. Each contestant's three event scores are added together to obtain that person's total score. The total score determines the order of the overall rankings.
1) Adam did not finish 5th in any individual event.
2) Bert finished 2nd in only one individual event.
3) Carl finished one position better in swimming than in cycling.
4) Doug finished 4th in only one individual event.
5) Eric did not finish 3rd in any individual event.
6) No contestant who won an individual event had the best overall ranking.
7) The contestant who finished 3rd in cycling finished better in swimming than the contestant who finished 3rd in running.
8) The contestant who finished 4th in running finished better in cycling than the contestant who finished 4th in swimming.
9) The contestant who finished 5th in swimming finished better in running than the contestant who finished 5th in cycling.
10) Only one contestant finished each event in a different position, and that contestant finished 4th overall.
Answer:The scoring system provides 10 points per event, or a total of 30 overall points. Since the overall winner did not win any individual event (clue 6) and Bert finished 2nd in one event (clue 2), that means that the best total score could only be 8 points (two 2nd place and one 3rd place). The only way to achieve 30 points with five unique scores, 8 being best, is 8 + 7 + 6 + 5 + 4 = 30.
Only the contestant who finished 4th overall had three different finishes, (clue 10), so the only way to achieve the proper overall point totals is as follows:
1st place (8 points) - 2nd, 2nd, 3rd (no 1st, 4th, or 5th individual finishes)
2nd place (7 points) - 2nd, 3rd, 3rd (no 1st, 4th, or 5th individual finishes)
3rd place (6 points) - 1st, 4th, 4th (no 2nd, 3rd, or 5th individual finishes)
4th place (5 points) - 1st, 4th, 5th (no 2nd or 3rd individual finishes)
5th place (4 points) - 1st, 5th, 5th (no 2nd, 3rd, or 4th individual finishes)
Adam did not finish 4th or 5th overall (clue 1). Bert finished 2nd overall (clue 2). Doug finished 4th overall (clue 4). Eric did not finish 1st or 2nd overall (clue 5). The contestant who finished 3rd in cycling is not the same as the one who finished 3rd in running (clue 7), so the contestant who finished 2nd overall had to finish 3rd in swimming. Carl finished one position better in swimming than in cycling, and the only combination that works is 2nd in swimming and 3rd in cycling.
Swimming: Eric, Carl, Bert, Adam, Doug
Cycling: Doug, Bert, Carl, Adam, Eric
Running: Adam, Carl, Bert, Doug, Eric
Overall: Carl, Bert, Adam, Doug, Eric
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