16 Math Problems for 2016
Yes, I know that I just posted some Math Problems for 2016 on December 19.
But I’ve decided to post some more for a variety of reasons:
- 2016 is cool.
- It’s a triangular number.
- It has lots of factors. (I’d tell you exactly how many, except that’s one of the problems below.)
- After writing the problems for that previous post, I just couldn’t control myself.
- It’s my blog, and I can do what I want.
People who write math problems for competitions (like me) love to be cheeky and include the year number in a problem, especially when any sufficiently large number will do. When the year number is critical to the success of a problem, well, that’s just a bonus. With that in mind, there are 16 problems below, each of which includes the number 2016.
A fully formatted version of these problems, complete with answer key, extensions, and solutions, is available for purchase through the link below:
Enjoy, and happy new year!
- What is the sum of 2 + 4 + 6 + 8 + ··· + 2016?
- Using only common mathematical symbols and the digits 2, 0, 1, and 6, make an expression that is exactly equal to 100.
- Find a fraction with the following decimal equivalent.
- How many positive integer factors does 2016 have?
- What is the value of n if 1 + 2 + 3 + ··· + n = 2016?
- Find 16 consecutive odd numbers that add up to 2016.
- Create a 4 × 4 magic square in which the sum of each row, column, and diagonal is 2016.
- Find a string of two or more consecutive integers for which the sum is 2016. How many such strings exist?
- What is the value of the following series?
- What is the units digit of 22016?
- Some people attend a party, and everyone shakes everyone else’s hand. A total of 2016 handshakes occurred. How many people were at the party?
- What is the value of the following expression, if x + 1/x = 2?
- A number of distinct points were placed along the circumference of a circle. Each point was then connected to every other point, and a total of 2016 segments were formed. How many points were placed on the circle?
- Let A = 1, B = 2, C = 3, …, Z = 26. Find a word for which the product of the letters is 2016. (This one may look familiar.)
- Each dimension of a rectangular box is an integer number of inches. The volume of the box is 2016 in3. What is the least possible surface area of the box?
- What is the maximum possible product for a set of positive integers that have a sum of 2016?
UPDATE: Bonus Material!
Special thanks to my friend Harold Reiter, who created the following 2016 problems for use as MathCounts practice:
- What is the smallest number N such that the product of the digits of N is 2016?
- What is the sum of the divisors of 2016?
- What is the product of the divisors of 2016? Express your answer as a product of prime numbers.
- Solve the following equation:
- What is the binary representation of 2016?
- What is the base-4 representation of 2016?
- What is the base-8 representation of 2016?