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Logic Grid puzzles come with a handy interactive grid that will help you solve the puzzle based on the given clues.


Puzzle ID:#37354
Fun:*** (2.76)
Difficulty:**** (3.32)
Submitted By:camrae27Aus****
Corrected By:MarcM1098




There is a new pizza place in town called Pick-A-Pizza. They have five wheels that, for just a few dollars, you can spin to decide the pizza chef, crust, cheese, meat topping, and veggie topping. When the wheels stop spinning, you have your pizza order! There have only been five customers so far, and each time, a different chef, a different crust (crisp, Greek, Sicilian, thin, or whole wheat), a different cheese (Gorgonzola, mozzarella, Parmesan, provolone, or Romano), a different meat topping (bacon, chicken, meatball, pepperoni, or sausage), and a different veggie topping (broccoli, mushrooms, olives, onions, or peppers) have been chosen. From the information provided, can you determine the crust, cheese, meat and veggie toppings on the pizza made by each chef?

1. The pizza topped with onions (which wasn't made by Nunzio) didn't have a Greek crust. Alfredo's pizza didn't have a whole wheat crust and wasn't topped with pepperoni. No pizza had both olives and mozzarella.

2. Mario didn't make the bacon pizza (whose crust was neither crisp nor thin). The sausage-topped pizza (which didn't have a whole wheat crust) didn't include peppers. Luigi's pizza (which didn't have a crisp crust) wasn't topped with broccoli.

3. Alfredo's pizza (which didn't include chicken) didn't have a Sicilian crust. Neither the pizza with a whole wheat crust (which wasn't topped with onions) nor Nunzio's pizza was topped with provolone cheese. Neither the pie topped with broccoli nor the pepperoni pizza was the one that had a crisp crust.

4. Neither Giuseppe's pizza nor the sausage pizza was the one topped with onions. The Sicilian pizza (which wasn't Luigi's) wasn't topped with peppers. Alfredo's pizza (which didn't include olives) wasn't topped with provolone cheese.

5. Mario didn't make the pepperoni pizza. The sausage pizza (which wasn't made by Nunzio) wasn't topped with mushrooms. The broccoli pizza was neither the one with a thin crust nor the one topped with mozzarella.

6. The meatball pizza (which wasn't topped with onions) didn't have a crisp crust. The olive pizza wasn't topped with Romano. Luigi's pizza (which didn't have a thin crust) wasn't topped with provolone.

7. The pizza with a Greek crust wasn't topped with broccoli. The bacon pizza had neither Parmesan nor Romano cheeses. There were no peppers on the thin crust pizza.

Open Grid Solver


Alfredo, Thin, Romano, Meatball, Mushrooms
Giuseppe, Whole Wheat, Mozzarella, Pepperoni, Peppers
Luigi, Greek, Parmesan, Sausage, Olives
Mario, Crisp, Provolone, Chicken, Onions
Nunzio, Sicilian, Gorgonzola, Bacon, Broccoli

The hints are not necessary to solve the puzzle. Here is an explanation of the first hint:

Luigi's crust is not crisp (clue 2), Sicilian (clue 4), or thin (clue 6), so it must be Greek or whole wheat. However, onions are not on the pizza with a Greek crust (clue 1) or a whole wheat crust (clue 3), so Luigi cannot have onions on his pizza.

That leaves only Mario or Alfredo who can have onions. Assuming Alfredo has onions leads to a contradiction: Alfredo did not use chicken (clue 3) or pepperoni (clue 1), and onions are not with meatballs (clue 6) or sausage (clue 4), so if Alfredo has onions, he must also have bacon. Alfredo does not have a Sicilian crust (clue 3) or a whole wheat crust (clue 1), and onions are not on the pizza with a Greek crust (clue 1), so he must have a crisp crust or a thin crust. However, bacon is not on the pizza with a crisp crust or a thin crust (clue 2), so Alfredo cannot have bacon. This is a contradiction, so the assumption that Alfredo has onions is false. Thus Mario has onions.


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Jul 12, 2007

This is the first logic-grid puzzle I have attempted that has all of its clues in a negative manner. I find myself stuck, I am a positive thinker, all of these 'neither, nor' and 'didn't includes' are killing my brain cells.
Jul 12, 2007

I hope my pizza is not this tough! I have ordered 4 times now and all I get is little red squares with x's. I will try again
Jul 12, 2007

Wow, I have no idea how to solve this one without the hint! Turned my brain upside down with all the negative clues. Great Puzzle!
Jul 13, 2007

Jul 13, 2007

After trying 5 times just using the clues, I have concluded that the 2 hints should be clues rather than hints. It doesn't seem to work otherwise.
Jul 13, 2007

As I was typing the above comment, Winner 4600 entered the comment "Brilliant." so I guess I am wrong.
Jul 13, 2007

I actually saw this teaser in the queue, so I don't remember if I used the hints or not. However, there were some corrections that needed to be made, so I submitted those along with changing the hints to the teaser body.
Jul 14, 2007

With the help of the hints, I was able to get the answer down to the point where I couldn't figure which cheese topping went with the thin and which went with the whole wheat . It seemed that either would work. The rest of the puzzle was solved. So I am not 100% convinced there is a unique solution. I would be grateful if anybody could help me here.
Jul 14, 2007

I thought it was great!
Jul 14, 2007

One more time: as it says under the title of the teaser, the grid is based on the given CLUES, not the Hints. This one shoud not have been allowed!
Jul 14, 2007

Yankee - The clues say that Broccoli is not with Mozzarella. So by the time you get to the Cheese toppings, you can see that Broccoli is with a Sicilian crust, and so the only crust left for Mozzarella is Whole Wheat. For the Thin crust, a clue says that it is neither Parmesan nor Romano, so Thin = Romano. You can PM me if you have any more questions...

By the way, I think I did use the hint to solve this one. It's being corrected.
Jul 16, 2007

Jul 17, 2007

Hurray! The clues are now all there (I hope). I say I hope, because I'm still having trouble solving this one. I am really enjoying the wording, though, which is very tricky. This is a good teaser!
Jul 18, 2007

This was very tricky. I still haven't figured it out yet.
Jul 18, 2007

Re-fixed - I moved clue #8 back to a hint where it was originally. I added an explanation in the answer showing how to logically figure out the first hint. The rest of the puzzle can be solved using similar logic.
Jul 20, 2007

Hard to believe, but I actually solved it! Sorry for the trouble I caused.
Aug 05, 2007

I figured out everything except for the cheeses... I'm so stuck!
Aug 15, 2007

After you get the part with the onions, everything else falls into place.
Aug 20, 2007

I found that the only way to get this one done was to use the hints.
Therefore, I think the hints should have been worked in as clues in some form. I don't believe it is possible to work a logic problem with only negative clues. I think that there must be at least one positive clue. Fun to work, hope you give us another one but with some positive clues added. Thanks.
Sep 20, 2007

Oh my!
This was so difficult! Took me all day to solve it. (off and on)

The fact that the entire puzzle was nearly all negatives made this very confusing and tough. I enjoyed every frustrating moment and came to the correct conclusion in the end.

Thanks for a great teaser!

And the cheeses can be determined: I think the last clue for cheese is that the broccoli pizza is not the one with thin crust nor the one with mozzarella. This tells us that the thin crust is a different pizza than the mozzarella. Therefore Alfred's thin crust pizza is not mozza and must be romano cheese.
Nov 25, 2007

Tough puzzle. Although I did not need the hints, I think the hint should say that the puzzle solution requires 'trial and error'.

(That suggestion goes for any logic-grid puzzle on this site.)
Jan 19, 2008

This puzzle was very hard (which I welcome!) but it was no fun at all There were not enough clues for the cheeses and even the answers were confusing to read since they were completely out of order. I never would have been able to solve this without the clues. Maybe it should have included a "The 5 pizzas are...." kind of clue
Nov 03, 2010

Terrific puzzle! And it is solvable without the hints or trial and error. It does take some insight that took me a few hours to see, and then the rest fell into place. To whoever said it isn't possible to solve a logic grid with only negative clues: that is not so. Clearly if you have a row or column in one box with 4 negatives, then you can mark a positive. The thing to do on a puzzle like this is to find combinations of clues that allow you to find more negatives, so that you can deduce a positive to get you going.
Jan 08, 2011

Jun 19, 2011

I figured it out great job! After trying this puzzle many times I finally got all the answers right.
Jul 23, 2012

Apr 24, 2013

Wow, I didn't find it that just look for other negatives like someone else said, then do a little trial and error. Thanks so much for your work, and for the challenge The only thing that drove me nuts was my own fault, I did all the work, then went to hit the answer link, and hit the show grid instead....erased everything So I got to do this one twice.
Jul 13, 2013

For those of you having trouble, remember that one rule of the English language is that whenever you don't have nothing, you have something.
Aug 24, 2014

Wow that was hard gosh. Αυτό ήταν πολύ σκληρό
Feb 03, 2016

I was shocked ... after puzzeling over the entry suddenly all fell into a complete grid ... so, the entry is tough after that nice and smooth ... i like it

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