Logic Puzzles

I love logic puzzles, the ones where a complicated problem is posed with a variety of stipulations and you have to find the arrangement that satisfies the given scenario without violating the rules. For example, seven botanists (Amber, Ben, Carlos, Devon, Emily, Frederick, and Giovanni) each hold one of three jobs at a greenhouse: pruning, watering, or fertilizing. No more than three people are responsible for the same job. Devon cannot work with Ben. If Amber does watering, Frederick does not do pruning…etc.

I’ve enjoyed these types of brain teasers ever since I was a young student and first encountered them in math class. After the initial exposure whet my appetite, I became a voracious consumer. Unlike readily available crossword puzzles, which I also enjoy, logic puzzles are much more esoteric. This is particularly frustrating for someone like me who gets single-mindedly obsessed with certain interests at a given time. I’ve learned that this hyper-focused fixation is a common trait held by those on the autism spectrum. It’s not always a good thing, because the drive to pursue only the obsession (termed a “special interest” by autism professionals) places such impenetrable blinders up on all sides surrounding the interest that even activities of daily living and biological needs can get ignored. Although this behavior seems diametrically opposed to the presentation of ADHD, at times, I’ve become so immersed in a special interest that I forget to eat or drink for much of a day. Some special interests seem to persist throughout life or at least for many years, while others are more intense and short-lived. Unfortunately, the latter can lead to forgotten purchases and forgotten clutter.

I’m lucky to have a job with such diverse and interesting assignments. The past two days, I’ve been tasked to develop logic puzzles and associated questions. As difficult as it can be to solve a logic puzzle, a challenge that I find thrilling, it’s that much harder to create them because you have to imagine all of the possible permutations and adapt the conditions appropriately to ensure that the solution for each question is the one and only unique answer. Tackling these types of assignments and turning in well-crafted, tricky puzzles brings me a deep sense of excitement and pride. I find that even when I’m trying to fall asleep at the end of the day, I’m running through scenarios from the exercises I wrote. If a movie festival is to screen six movies from ten available features, and exactly two movies must be played from each of three genres (comedy, drama, and action)…Then the etch-a-sketch screen in my brain starts sketching a rough grid for the problem, to start working through possibilities to satisfy the rules.

It’s not often that I get this specific type of assignment, but every so often when the opportunity rolls around, it’s like seeing a long-lost friend. I am instantly reminded how much I love them and how lucky I am to have a job that requests them on occasion, and a crazy brain that seems to receive a nearly unparalleled jolt of joy when working on them.

For anyone who enjoys them too, I’ve included one below that I made. If you want to check your answers, you can email me at ambersayer(at)gmail(dot)com

A pizza shop owner makes fresh pizzas every morning one at time before opening her doors at 11:00AM for the lunch rush. There are currently seven fresh pizza topping options on her menu: basil, chicken, olives, eggplant, mushrooms, peppers, and tomatoes. To ensure the pizzas are prepared in a logical order according to demand, preparation time, recipe yield, and oven time, the following conditions must be satisfied:

• If the mushroom pies are made earlier than the olive ones, then the basil pies must be made later than the tomato ones.
• The chicken pies are made second or sixth.
• Exactly two pizzas must be made between making the olive pies and the chicken pies.
• If the mushroom ones are made later in the morning than the olive pizzas, then the basil ones must be made sometime before the tomato pizzas.
• The olive pizzas are made earlier than the tomato or the pepper ones, but not both.
• The basil pizzas must be made immediately before or immediately after the chicken ones.

1. Which one of the following could be the order in which the pizzas are made from first to seventh?
a. Basil, chicken, tomatoes, olives, mushrooms, peppers, eggplant
b. Mushrooms, eggplant, olives, tomatoes, basil, chicken, peppers
c. Peppers, eggplant, olives, mushrooms, basil, chicken, tomatoes
d. Eggplant, chicken, peppers, basil, olives, mushrooms, tomatoes
e. Tomatoes, chicken, basil, eggplant, olives, peppers, mushrooms

2. Which one of the following pizza types CANNOT be made fifth?
a. Basil
b. Peppers
c. Tomatoes
d. Mushrooms
e. Eggplant

3. The exact baking order of all seven pizza flavors can be determined if which one of the following is known?
a. The basil ones are made third, and the tomato ones are made sixth.
b. The pizzas with peppers are made first, and the chicken ones are made sixth.
c. The mushroom pies are made second, and the tomato ones are made fourth.
d. The basil pizzas are made third, and the eggplant ones are made fourth.
e. The pepper pizzas are made first, and the mushroom ones are made sixth.

4. Which one of the following is a complete and accurate list of the possible slots in which the mushroom pizzas could be made?
a. First, fourth, sixth, seventh
b. First, second, sixth, seventh
c. First, second, third, fifth, seventh
d. First, second, fifth, sixth, seventh
e. First, second, fourth, sixth, seventh

5. Which one of the following could be a possible partial list of the order in which the pizzas are made?
a. Basil, chicken, and mushrooms as first, second, and third, respectively
b. Peppers, tomatoes, and olives as first, second, and third, respectively
c. Chicken, basil, and tomatoes as second, third, and fourth, respectively
d. Mushrooms, olives, and tomato as fourth, fifth, and sixth, respectively
e. Basil, chicken, and mushrooms as fifth, sixth, and seventh, respectively

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