Happy Thanksgiving everyone. I hope you are having a wonderful day. Here are a few questions that may arise for some of you today, see if you can find the correct answers!

While trying to answer these, take some time to check out our STEM and leaf Holiday Gift Guide. We have some great suggestions for STEM inspired toys that will be a big hit this holiday season.

### #1 Suppose that you have six people that will be joining you for dinner. You will be seated at a table that looks like the one below. We will consider arrangements the same as long as the same people are next to each other, and the same two people are sitting at the end chairs. How many distinct ways can the six people be seated at the table?

#### #1 bonus. What is the probability you are seated next to someone you wouldn’t like to be?

### #2a Suppose that you had 10 people coming over. You are going to arrange the seating so that 6 people sit at the main table and 4 sit at the kiddy table. How many arrangements of the 10 people are there, assuming arrangement are only distinct if there are different people at each table.

#### #2b bonus. What is the probability you will have to sit at the kiddy table if seats are assigned randomly?

### #3 Justin, Jaci and Joey share a 4 pound turkey. Justin eats twice as much as Jaci, and Joey eats half a pound more turkey than Jaci, how much turkey did each person eat?

### #4 Since it is thanksgiving, you plan on eating all day long. However, you will be snacking while the meal is being prepared and eat a lot when the meal is finished, then continue to snack until you fall asleep in food coma. Suppose that you start eating at 8:00 AM and fall asleep at 8:00 PM. The rate at which you are eating, in calories, can be modeled by \(c(t)=\frac{1}{4}t^{4}-6t^{3}+36t\) where \(t\) is the number of hours since 8:00 A.M. How many total calories did you consume throughout the course of the day?

### #5 You go up for desert and take \(\frac{1}{3}\) of the pumpkin pie for your first serving. You want more, but not quite as much, so for seconds you take \(\frac{1}{3}\) what you took the previous time. Instead of stopping, you keep going back for more each time taking \(\frac{1}{3}\) the previous amount. How much total pie will you eat (if you could indeed continue this forever)?

### #6 Some cut up one of the pumpkin pies already and cut the pie into 3 inch by 3 inch square pieces. You are tasked with cutting the second pie, but you want to cut it into slices. However, you want them to have the same amount of pie per slice as the square pieces had. If the second pie has a diameter of 12 inches, what would be the angle covered by the slice of pie?

Submit answers below in order to find out how well you did!