9/20/2013 11:20:44 AM
cantsolve Posts: 4

Hello Everyone, I'm new to the world of Logic puzzles. I'm trying to work on my first one but seem to be stuck. can someone please solve this along with the proper procedure of solving? Thanks everyone
here's the problem:
On Police Officer Appreciation Day at the Bear Clause Donut Shop and Law Firm, all local officers who stopped by in uniform got to eat as many donuts as they wanted. 30 men and women in blue showed up and chowed down.When the cloud of powdered sugar finally settled and the satisfied officers left, the clerk realized she had forgotten to write down how many donuts each officer had eaten. The legal branch of the Bear Clause Donut Shop and Law firm informed her that because of some quirk in the law, she must report the total number of officers who ate 6. 7, 8, or 9 donuts so those baked goods could be written off as charitable donation. All the poor clerk could remember was that 10 of the officers ate fewer then 6 donuts, 8 ate more than 7 donuts, 5 ate more than 8 donuts, and 1 ate more than 9 donuts. Can you help the clerk stay out of trouble with her bosses by figuring out the total number of officers who ate 6,7,8, or 9 donuts?

9/20/2013 1:46:42 PM
Frances Posts: 698

As far as I could figure, the clerk didn't remember enough to stay out of trouble with her bosses. From what we're given: There's no way for me to tell how many (if any) ate either exactly 6 or exactly 7 donuts. Of the 8 that ate more than 7, could any of them have eaten, say, a dozen? Did the officers not mentioned in the clues eat any donuts at all? There just doesn't seem to be sufficient information for me to determine much of anything. Maybe I'm just missing how to approach this. Sorry. Anyone else? edited by Frances on 9/20/2013

9/20/2013 3:53:13 PM
Purple Pisces Posts: 878

I think I solved it, but don't want to give the answers in case you are a student. Forgive me for being a little suspicious.
All you need to figure out this problem is basic math. For a start I will say that to help you find the number of officers who ate 6 or 7 donuts you just need to look at the info given about who ate less than 6, and who ate more than 7.

9/20/2013 4:40:40 PM
Frances Posts: 698

Are we looking for just the total officers who ate betwen 6 and 9 donuts (which maybe could be broken into two groups), and not how many per each amount? I could make more sense of that.

9/20/2013 4:44:15 PM
cantsolve Posts: 4

Thanks Purple Pisces for the hint. I'm definitely not a student lol. My wife and I bought a book of puzzles and this is one that we are stuck on. According to the information given 10 ate fewer than 6 which means out of the 30 total officers 10 can be eliminated from having 6,7,8, or 9 donuts. 1 ate more than 9 which means that which means that out of the remaining 20 officers 1 can be eliminated from having 6,7,8, or 9 donuts. So now we're down to a possible 19 officers. This is where I get stuck.... 8 ate more than 7....to me this means 8 officers could have eaten 8,9,10,11,12,13,etc. donuts 5 ate more than 8. ...to me this means 5 officers could have eaten 9,10,11,12,13,14,etc. donuts 8+5=13..what about the other 6 officers?
can you tell me your thought process in solving this?

9/20/2013 4:48:21 PM
cantsolve Posts: 4

by the way I do have access to the answer (it's in the back of the book lol) but I want to know how to solve the problem.

9/20/2013 5:01:53 PM
cantsolve Posts: 4

Frances, that's a good question. Now that you brought this up I'm wondering the same thing. The questions reads "total number of officers who ate 6,7,8, or 9 donuts?" I'm not sure if they're asking for the total number of officers who ate between 6 and 9 or the individual number of officers who ate 6,7,8,9 donuts....it's definitely not clearly put..maybe puple pisces can let us in on his solution

9/20/2013 5:54:18 PM
Frances Posts: 698

cantsolve wrote: "8 + 5 = 13...what about the other 6 officers?"
If we assume that some officers must have eaten 6 and some must have eaten 7, well, there they are I guess. While I just don't get that from the clues, maybe that's it. Likewise, in "8 ate more than 7", we may have to assume it means "but not more than 8" or they would be included in the "more than 8" group. If so, I think there's too much assumin' going on for me.

9/20/2013 6:28:49 PM
Purple Pisces Posts: 878

Deleted my earlier post thinking I had it solved, but realized I messed up somewhere. Will work on it some more and get back to you guys. Sorry for the mix up! edited by Purple Pisces on 9/20/2013

9/20/2013 8:37:21 PM
Purple Pisces Posts: 878

In my original post I had posted the officers as being 6,7,8 and 9 instead of the donuts. Correcting myself, I still get the same numbers I just had to switch them to correspond to either donuts or officers.
The most I can conclude as far as the 6 and 7 donuts is that a total of 12 officers ate 6 or 7 donuts. There are 30 officers, 10 ate less than 6 and 8 had more than 7. So 18 officers either had less than 6 or more than 7. 3018=12 officers who either had 6 or 7 donuts. Now for some reason I divided this number evenly so that 6 officers had 6 donuts and 6 officers had 7, but from the clues I can't be certain the correct numbers. But we do know that 12 officers are responsible for eating either 6 or 7 donuts.
Cantsolve was right about the 19 officers. Accounting for the 12 officers 1912=7 officers ate either 8 or 9 donuts.
8 officers ate more than 7 (8 or more) donuts  the 5 officers who ate more than 8 (9 or more donuts) This leaves 3 officers who ate 8 donuts
5 officers who ate more than 8  the 1 who ate more than 9 = 4 officers who had 9 donuts
6+6+3+4=19 officers 19+10 (those who had less than 6)=29 plus the 1 who had more than 9=30 officers.
The more I look at this puzzle the more I'm doubting my answers so I'm very glad that you have the solution in the back of the book. Sorry for any confusion I may have caused you cantsolve, Frances and anyone else who is working on this puzzle.
Ally edited by Purple Pisces on 9/20/2013

9/21/2013 9:04:17 AM
Indiana Puzzler Posts: 559

Purple Pisces wrote:
In my original post I had posted the officers as being 6,7,8 and 9 instead of the donuts. Correcting myself, I still get the same numbers I just had to switch them to correspond to either donuts or officers.
The most I can conclude as far as the 6 and 7 donuts is that a total of 12 officers ate 6 or 7 donuts. There are 30 officers, 10 ate less than 6 and 8 had more than 7. So 18 officers either had less than 6 or more than 7. 3018=12 officers who either had 6 or 7 donuts. Now for some reason I divided this number evenly so that 6 officers had 6 donuts and 6 officers had 7, but from the clues I can't be certain the correct numbers. But we do know that 12 officers are responsible for eating either 6 or 7 donuts.
Cantsolve was right about the 19 officers. Accounting for the 12 officers 1912=7 officers ate either 8 or 9 donuts.
8 officers ate more than 7 (8 or more) donuts  the 5 officers who ate more than 8 (9 or more donuts) This leaves 3 officers who ate 8 donuts
5 officers who ate more than 8  the 1 who ate more than 9 = 4 officers who had 9 donuts
6+6+3+4=19 officers 19+10 (those who had less than 6)=29 plus the 1 who had more than 9=30 officers.
The more I look at this puzzle the more I'm doubting my answers so I'm very glad that you have the solution in the back of the book. Sorry for any confusion I may have caused you cantsolve, Frances and anyone else who is working on this puzzle.
Ally edited by Purple Pisces on 9/20/2013
THAT'S A LOT OF DONUTS! LOL

9/21/2013 12:58:35 PM
Purple Pisces Posts: 878

I think I scared away cantsolve and Frances LOL!
Thinking about this puzzle some more I could see it as being solvable for the officers who ate 6 or 7 donuts if there were 2 clues or rules which stated:
1) No group of officers contains the same amount of individuals as any other group. This would eliminate the possibility of the ones who ate 6 or 7 donuts from being 6 and 6. It would also eliminate the possibility of it being (3 and 9) or (4 and 8) as the 3 and 4 are already the total amounts for the officers who ate 8 or 9 donuts. This leaves 5 and 7 , which brings me to the next rule:
2) The number of a group of officers cannot be the same as the amount of donuts that group ate. Which would put 7 officers eating 6 donuts and 5 officers eating 7 donuts.
This post is hypothetical, and just pointing out how I could see these rules as helping to solve the puzzle. Other then these types of clues/rules I cannot figure out how the number of officers who ate 6 or 7 donuts can be clearly determined.

9/21/2013 2:03:02 PM
Frances Posts: 698

Well, at least we've all pretty well stated the things that are wrong with the presentation of this puzzle! LOL You've done a good job with your math and logic, Purple, considering the incomplete (in my opinion) clues. And I wonder if we may be just overthinking it in our desire to pin down all the numbers exactly, when it might not be necessary. I'm not sure. The one answer I can say for certain is "19".

9/21/2013 2:35:40 PM
Purple Pisces Posts: 878

Thanks Frances! It makes me wonder too if we're overthinking this puzzle. I hope that cantsolve will post again and share the answer with us.

9/21/2013 11:43:14 PM
Semipro Posts: 292

I'm late to the party, but I'll point out something else that's flaky about this puzzle. It calls doughnuts "baked goods." No! Doughnuts are FRIED!

9/22/2013 8:49:15 AM
Indiana Puzzler Posts: 559

Frankly, this puzzle doesn't seem to come across as having the high standards that Penny Logics usually display. I wonder what the source is.

9/22/2013 12:29:45 PM
Purple Pisces Posts: 878

I was wondering where this puzzle came from too Chris! Interestingly, I googled the first couple words of the problem and found only one other listing on the internet besides the forum here. It was someone asking for help with it on Yahoo and they included those all telling four letters....ASAP!! The person who answered could not figure the exact figures for 6 and 7, only that combined it equaled 12.
Here's the link: http://answers.yahoo.com/question/index?qid=20111126084625AAEioY5

9/22/2013 9:57:36 PM
Semipro Posts: 292

I was wondering what company published it, too. Besides not being very clear, it isn't written in PP's style.

9/23/2013 12:29:53 PM
Amy Lowenstein Posts: 1599

I guess "cantsolve" figured we on the Penny/Dell forum would be more likely to help solve this logic puzzle, than other places they could have questioned. Even if the puzzle turns out, indeed, NOT to be one from Penny or Dell, when "cantsolve" found our forum on the Internet, they figured this was a good place to ask!
 Amy

9/23/2013 8:28:29 PM
Semipro Posts: 292

It IS a good place to ask. The source of the puzzle may not even have a forum.
