A boxing tournament was scheduled in a distant island, and seven inhabitants registered for the competition. Each contestant was to box with each of the others, and each boxer's number of wins would be totaled to determine the winner, and the rankings of the 6 runner-up boxers.
- Ian finished ahead of Gary, but behind Vince.
- Each of the ranks of Abel and Vince was an odd number.
- Each of Brad and Abel finished behind Ian .
- Sam had precisely four wins.
- Hal finished two places behind Brad .
- Gary finished two places ahead of Abel.
In which order did the boxers finish, and how many wins did each have?
Note: There were no ties, either in any individual match or in the final standings.
1. Because there were no ties in the matches or standings, the 1st place had 6 wins, the 2nd place had 5 wins. The 3rd place had 4 wins, etc.
2. From Clue 4, Sam is therefore 3rd place.
3. The other odd places (1st, 5th and 7th) belong in some order to Abel and Vince (from clue 2) and therefore Gary (from clue 6). From clues 1, 3 and 6, Vince finished ahead of Ian and Gary finished behind Ian and ahead of Abel. So the order must be Vince 1st, Gary 5th, and Abel 7th.
4. That leaves Ian, Brad and Hal in 2nd, 4th and 6th in some order. From clues 3 and 5, Ian is ahead of Brad who is ahead of Hal, so that is in fact the order.
Final answer therefore is Vince, Ian, Sam, Brad, Gary, Hal and Abel with 6, 5, 4, 3,2, 1 and 0 wins respectively. (And the only way this can happen is if every boxer defeated the boxers who ranked below him and lost to the boxers ranked above him. So we also know the result of all the individual matches.)
NOTE: The puzzle is solvable if clue 5 is just "Hal finished behind Brad". I never used the "two places" information.
Edited on September 13, 2012, 11:58 pm
Logical Explanation (spoiler) and TMI
