Logic Grid puzzles come with a handy interactive grid that will help you solve the puzzle based on the given clues.
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.
HintYou must first determine the five unique point totals necessary to determine the overall standings.
Then you must determine what combination of individual finishes are necessary to achieve those overall point totals.
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
Jan 19, 2008
|Another good teaser! It was too much for me...I couldn't finish it. I'll give it another try later when my brain gets some rest. |
Jan 26, 2008
|Absolutely, the most difficult logic grid puzzle I have ever done. It took me hours over several days. Well designed, fun to do, and so many interlocking clues. It is beyond me how someone crafts such a puzzle. Congratulations!! |
Mar 07, 2008
|quick comment - I haven't looked at the solution, but the hint declares that each participant has a UNIQUE point total. If that is a requirement, then it should be noted in the problem description. (otherwise, one of my possible solutions was to see if 8,7,5,5 and 5 would work)|
Mar 09, 2008
|cnmne, once again a fabulous puzzle!! (see my comment above concerning the unique point solutions) Once I figured out the finish combinations for each person, the rest of the puzzle fell into place. |
Mar 21, 2008
|Another excellent logic teaser! To mom_rox: clue 10 indicates that someone finished in 4th place overall - a 3-way tie for 3rd wouldn't satisfy that requirement.|
Mar 31, 2008
|Gizzer - thanks for clearing that up for me. |
Apr 03, 2008
|Wow, that was way over my head. That's the best kind (though I'll never get it)!|
Jul 16, 2008
|WOW! I couldn't finish that one, hehe. Thanks so much for explaining it in the answer how you figured that out. |
Sep 01, 2008
|That was one of the best (if not THE best) logic grids I have ever done. Ever. Wonderful job! |
Dec 15, 2008
|I actually wrote a macro in VBA to solve this one. It was taking me too long by hand.|
Dec 25, 2008
|That was great! It took over an hour, but I finished it without the hint. |
I do think, though, that the puzzle should have explicitly stated that no two people had the same overall score. That isn't a given--the answer could have listed multiple people with the same overall score without violating any statements. I started solving it without the grid and it was only after seeing the grid that I realized that no ties for overall must be a constraint. By this time I knew there had to be an additional constraint on the possible finish combinations. Without this constraint the puzzle has multiple solutions.
Dec 25, 2008
|Guess I shoud have read the rest of the comments first regarding why there could be no ties for overall. |
Aug 28, 2009
|Wow! What a fabulous puzzle. It took forever, but what fun! Congratulations on a fine teaser!!|
Oct 31, 2010
|I really enjoyed this puzzle. It came together well once I abandoned the grid and reasoned it out the same way the answer describes -- definitely took some thinking, though! (I did assume there were no ties, both because I'd already looked at the grid and because the puzzle clearly wouldn't have a unique solution otherwise.) I don't see that the grid serves much purpose in doing this puzzle.|
Dec 02, 2010
|The scoring system discussed in your answer does not appear to match the scoring system given in the teaser.|
May 01, 2012
|I finally got it! Once I finally got the scoring down it was a snap, but man oh man was that scoring a big issue. Thx for making my brain kick into overdrive! |
Feb 15, 2013
|As someone else said, this is one of the BEST puzzles I've ever done, and that includes magazines! When I saw how little could be done initially with the grid, I used the hint, which really was a great hint without giving anything away. I'm not stupid, but narrowing down possibilities with math is (so far, anyway) rarely used on this site I LOVED it!! The clue stating that no individual winner took 1st place over all eliminated half the possibilities, and (in my deductions) only left 3 places for 1st place to be used: (points) 4,1,1; 4,1,0; and 4,0,0. With that and the clue stating someone only took one 2nd place, that could only leave 3,3,2; and 3,2,2 as the other point combinations. It didn't occur to me to add up the total possible points to begin with, but seeing the comments, it looks like I wasn't alone in that . However, the point totals 8 thru 4 in sequence made over all placement clear, and the grid helped with who came in what place individually. HUGE amount of fun to solve, thank you so much for your work!!|
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