Probability, Counting & Combinatorics
Santiago baked gingerbread cookies in the shapes of children. He gave each gingerbread boy and girl eyes made from chocolate covered candies in one of four different colors, a nose made from a butterscotch chip, toffee chip or peanut butter chip, and a mouth made from a piece of red licorice. Santiago then gave each gingerbread boy and girl buttons made from gum drops in one of four different flavors. For the final detail, he gave each gingerbread boy a blue bow tie, and each gingerbread girl a red hair bow.
It’s Autumn, and that means leaves are falling! Amber’s house occupies 2650 ft2 in the middle of a 50-foot by 80-foot parcel of land, and the leaves that fall cover the ground all around her house. If it takes Amber’s family 4.5 hours to rake all the leaves, how many square feet of leaves did they rake each hour?
Each week, Devin buys school lunch on Friday because the cafeteria serves pizza every Friday. Monday through Thursday, Devin brings his lunch to school. The lunch he brings always includes a peanut butter and jelly sandwich, a fruit and a drink. Devin has enough fruit and drink options to make a different lunch every day that he brings lunch for the next four weeks. If Devin has the same number of fruit options as he has drink options and he takes no days off from school, how many different fruit options does he have?
A new school year often means new school clothes, new teachers and new friends. One of our favorite parts of a new school year is the release of a new MATHCOUNTS School Handbook! Download your free copy after solving a few problems from some previous handbooks.
Lily is going to the movies with Abby, Bea and Jaclyn. Abby wants to sit at the end of a row, and Bea only cares that she is seated next to Jaclyn. In how many different ways can the girls be seated in a single row that has only four seats?
Nona went shopping to buy some new school clothes. At the first store she bought two pairs of pants, each originally priced $30. Nona used a coupon that reduced the price of each item by 15%, and then a 5% sales tax was applied to the new subtotal. What was the total purchase price?
The summer months are the most popular time to move to a new home. Janet’s family is moving, and she suddenly realizes just how much stuff they have in their current home. Once the moving company finishes packing everything in boxes, they begin the task of numbering them. A sticker is placed on every box and on every item that is too large to fit in a box. Janet notices that stickers in three distinct colors are used. There are blue stickers numbered 239 through 262, green stickers numbered 163 through 178 and yellow stickers numbered 453 through 492.
A tree shades part of a rectangular table, as shown, so that two seats are in the sun and two are in the shade. Will, Xavier, Yvette and Zoe are in search of a place to sit and enjoy their lunches. If Yvette insists on sitting in the shade, and Zoe refuses to sit next to Will, how many different arrangements are there for Will, Xavier, Yvette and Zoe to be seated at this table?
The summer has unofficially begun for many families around the country, so here are a few problems related to Miranda’s family vacation.
When packing for the trip Miranda didn’t want to bring a lot of extra clothes, so she packed 4 shirts, 2 pairs of shorts and 1 skirt (all of which coordinate). If an outfit consists of a shirt and a pair of shorts or a skirt, how many distinct outfits did Miranda pack?
Last week the National Competition concluded, and Luke Robitaille from Texas became the first ever two-time MATHCOUNTS National Champion. Let’s look at some of the problems he had to solve on the way to the top!
On Sunday, May 13th, 224 middle-school math students participated in the written rounds of the 2018 Raytheon MATHCOUNTS National Competition. On Monday, May 14th, the top 12 competitors will go head to head in the National Countdown Round to determine the 2018 MATHCOUNTS National Champion. Let’s solve a few problems from the 2017 National Countdown Round.