Comments (16)

1. Should it be that Phil ate a third of all pretzels eaten?

   posted by David on 12-7-2009 at 8:01 am

2. I thought the \nine pretzels between them\ meant there was a difference of nine pretzels, and got the following answer. Either way, good puzzle!

   Cliff- 14
   Phil- 10
   Frasier- 7
   Paul- 5
   Norm- 4

   posted by Jenna on 12-7-2009 at 8:33 am

3. Hi Sandy,
   Can you please show how to arrive at your solution?

   posted by KJ on 12-7-2009 at 8:39 am

4. I got a different solution because I thought there were only six letters in Frasier’s name. Obviously, I need more coffee.

   posted by Erik on 12-7-2009 at 8:46 am

5. There a fifth clue that everyone should’ve known……**spoiler alert**…..how is anyone but Norm not winning this contest?!?!?

   Cliff and Paul are easy to figure out….from there, clue #3 was my catalyst for the remaining answers.

   SANDY’S NOTE: Norm had to stuff his face in the last few seconds to win, J. At first, he spent much more time washing down the pretzels than eating them. :)

   posted by J on 12-7-2009 at 8:49 am

6. Jenna, I assumed that saying “neck-and-neck” would make it clear that there wasn’t a nine-pretzel difference between the two of them… but, to be safe, I adjusted the text to say “combined” to avoid any further confusion. Thanks for pointing that out!

   posted by Sandy Wood on 12-7-2009 at 9:30 am

7. KJ, here’s probably the quickest way:

   Per clue #2, Paul ate 5 pretzels, and Cliff ate 4. (If these numbers were reversed, it would conflict with rule #3).

   Since Cliff ate 4 pretzels, neither Norm nor Cliff could have eaten 4 pretzels, since no two competitors ate the same number. This means neither of them fit rule #3 as well, leaving Frasier as the one who ate a number of pretzels equal to the letters in his name, 7.

   We know Frasier ate half as many pretzels as the winner, so the winner had 14. SO we have 14+7+5+4 – 30 pretzels eaten so far.

   So, solving for clue #4, Phil had 10 pretzels. This would move the total to 40, and give him one-quarter of the total pretzels.

   Hope that helps!

   posted by Sandy Wood on 12-7-2009 at 9:36 am

8. I don’t know…this one confuses me a lot.

   I was on the right track at first. Cliff didn’t eat five, Paul didn’t eat four. Then I thought “Norm & Phil couldn’t have eaten four either” which got me that Fraser was the only one left who could have eaten the same number as his name, so he ate seven and the winner ate fourteen.

   I probably could have solved and got the solution given from that, but then I thought about it some more. Why can’t either Norm or Phil have eaten four? Regarding Phil, four might not have been 1/4 of the total, but why not Norm? My original thought was that if one of them ate four, the other would have had to also, but that’s not in the clues.

   So I looked at the solution, which leaves me with another question:
   How do I know that Cliff and Paul ate 4 & 5 respectively? Why didn’t they eat six and three? Or seven and two?

   The only way I see to get to the answer is to make a lot of assumptions that aren’t held up in the clues. Am I missing where they’re held up?

   Overthinking, yes, that’s me.

   SANDY’S NOTE: R.M., note that the Cliff/Paul clue reveals that they were “neck and neck” throughout the contest; this makes it clear that their scores were 4/5 or 5/4 instead of 3/6 or anything else. Reviewing the text intro should alleviate the rest of your confusion. There, it stipulates that no two contestants consumed the same number of pretzels. So since Cliff ate 4 pretzels, we know that Paul, Phil, and Norm did NOT have 4.

   posted by R.M. Koske on 12-7-2009 at 9:43 am

9. I think the fact that none of them finished with the same total or ate zero is unnecessary information although it does greatly simplify the solution.

   Cliff eating 4 and Paul eating 5 were obvious. Since Frasier finished with half of the winner clearly he didn’t win nor did Cliff or Paul (you can’t half half of 5). So the winner must have been Phil or Norm. Phil could not have won while managing to only eat 1/4 of the total. He would have needed to eat at least 6 to win, but that would mean the other competitors only could eat a maximum of 17 (5 for Paul, 4, for cliff, 3 for Frasier, and 5 for Phil). So Phil could not win, this means that Norm must have won. Further it means that Norm did not eat the same number as letters so either Phil or Frasier must have eaten the same as their letters. Since Phil would only consume 4 if he matched his letters, that wouldn’t be enough to be 1/4 of the total which would be a minimum of 22 (4 for Phil, 5 for Paul, 4 for Cliff, 6 for Norm, and 3 for Frasier). So Frasier must have matched his letters. So we know Frasier had 7, Norm had 14, Paul had 5, Cliff had 4, and Paul must have had 10 to make the 1/4 total true.

   posted by Thomas on 12-7-2009 at 11:16 am

10. I don’t understand why Phil couldn’t have eaten any number from 8-13. If he had the total is 32, he had 8, if the total is 36, he had 9, and so forth, but he couldn’t have had as many as the winner. Am I missing something very basic here? 8 is exactly one quarter of 32, right?

    posted by Zac on 12-7-2009 at 1:42 pm

11. Zac, if you follow my logic on the post before yours then you see that Norm must have won the competition with 14, Frasier must have had 7, Paul must have had 5, and Cliff must have had 4. In total those 4 competitors ate 30 pretzels. If Phil ate 8 pretzels then 28 would have been eaten. The only number that allows Phil to eat exactly 1/4 is 10.

    posted by Thomas on 12-7-2009 at 1:58 pm

12. I meant 38, sorry for the typo.

    posted by Thomas on 12-7-2009 at 1:59 pm

13. I had the same logic as Sandy up through determining Norm, and then did some quick algebra at the end to find out Phil’s rations. Pretty pleased with myself actually – I’m way better at logic puzzles than word puzzles!

    However, I did make the assumption that only whole pretzels were consumed. And the “neck and neck” bit was a little confusing; they could be neck and neck NEAR the end, but if they were so AT the end, then it would be 4.5 each.

    posted by Stephanie on 12-7-2009 at 2:57 pm

14. The puzzle has a flaw if we assume the contest participants are not limited by stomach volume – Phil could have eaten 100 pretzels from a 400 pretzel total with Cliff eating 4 and Paul eating 5, Frazer eats 97 and Norm wins with an unbelievable 194 pretzels eaten in one minute!

    Zak, Phil could not have eaten 8, because that would leave (with 9 from Cliff and Paul) 15 pretzels between Frazer and Norm. While 5 and 10 respectively could be a solution, Paul has already eaten 5 pretzels, so this violates the second condition. If Phil ate 9, that would mean Frazer ate 6, which violates rule # 3 (no 6 pretzels for Frazer). Everything above 9 for Phil works though…

    posted by Dotty on 12-8-2009 at 12:46 pm

15. eh, never mind – I’m ignoring rule # 3.

    posted by Dotty on 12-8-2009 at 1:22 pm

16. Hmmm Frasier ate 7, Paul ate 5, Cliff ate 4, Phil ate 10, Norm ate 14.

    Now let’s check. :D

    posted by Karen Tehani on 12-9-2009 at 3:24 am

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