## Archive for January 1, 2016

### 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:

**16 Problems for 2016 — just $1**

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 2
^{2016}?

- 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**in^{3}. 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?