Sequences and Patterns

This Saturday’s date, 02-10-18, forms an arithmetic sequence since 2 + 8 = 10 and 10 + 8 = 18. In honor of this occurrence, try your hand at solving these problems involving sequences and patterns.

 

What is the tenth term of the sequence −50, −49, −47, −44, −40, …?

Labor Day

Labor Day is a product of the American labor movement and is dedicated to the social and economic achievement of American workers. In honor of this day and the American worker, let’s solve some Labor Day themed math problems!

 

Let's Use Logic

The following are answer choices to a multiple choice question. If only one of the answers is correct, which letter choice must be the correct answer?

Binary Math

Binary math is math in base 2, instead of our typical base 10. All digits are 0s or 1s. Explore base 2 math in the following problems. The last one is a challenge, but if you get it, then you’ll have a trick for guessing numbers!

What is the value of 31 in base 2?

Parents' Day

We all know Mother’s Day and Father’s Day, but did you know Sunday, July 23rd was Parents’ Day? If you forgot, then maybe you can solve these problems about parents to show yours how smart you are!

At the school fair, MATHCOUNTS parents sold chocolate and vanilla ice cream as a fund-raiser. Forty bowls of chocolate ice cream were sold for $2.15 per bowl. Bowls of vanilla ice cream sold for $1.90 each. How many bowls of ice cream were sold if the total amount of money collected was $158.20?

Some Math with JULY

When the letters of the alphabet are assigned their integer values (A = 1, B = 2, C = 3, …, Z = 26), the word-product for JULY is the product of the letter-values for each of the letters in JULY.  When the square root of JULY’s word-product is put into its simplest radical form of ab, where b has no perfect-square factors greater than 1, what is the value of b?

2017 National Competition

Last week the National Competition concluded, and Luke Robitaille from Texas became the 2017 MATHCOUNTS National Champion. Let’s look at some of the problems he had to solve on the way to the top!

What is the maximum possible absolute difference between a two-digit integer and the two-digit integer resulting when the digits are reversed?

We want the largest possible two-digit integer and the smallest possible two-digit integer that have their digits reversed. These are 91 and 19. The difference is 91 – 19 = 72.