## Posts tagged ‘2016’

### AWOKK, Day 7: KenKen Puzzle for 2016

Good day, and welcome to Day 7 of the A Week of KenKen series. If you’ve stumbled onto this page randomly, you should definitely check out some of the fun we’ve had previously…

Well, here it is, September 25, a mere 269 days into the year, and I am only now presenting you with a KenKen puzzle based on the year. I suppose I can take some solace in the fact that I’m presenting the following 2016 KenKen puzzle before the year is over. Little victories.

You might note that the puzzle has the following attributes:

• The numbers 2, 0, 1, and 6 are featured prominently as individual cells.
• Every target number uses (some combination of) the digits 2, 0, 1, and 6.
• There are two large cages — one in the shape of a 1, the other in the shape of a 6 — each with a product of 2016.

This puzzle follows the standard rules of KenKen, but there is one major exception: although it is an 8 × 8 puzzle, instead of using the digits 1‑8, it uses 0‑7. (Puzzles that use an atypical set of numbers are known as KenKen Twist.) If you’re stuck, just fill in the squares randomly. There are only 108,776,032,459,082,956,800 different Latin squares of size 8 × 8, and your chances of guessing correctly are even better since 4 cells are already filled in.

As is typical of all puzzles presented on this blog, I am not posting the solution. At least, not yet. Maybe someday. If you beg. Or send me money. But not today.

### 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!

1. What is the sum of 2 + 4 + 6 + 8 + ··· + 2016?
1. Using only common mathematical symbols and the digits 2, 0, 1, and 6, make an expression that is exactly equal to 100.
1. Find a fraction with the following decimal equivalent. $0.\overline{2016}$

1. How many positive integer factors does 2016 have?
1. What is the value of n if 1 + 2 + 3 + ··· + n = 2016?
1. Find 16 consecutive odd numbers that add up to 2016.
1. Create a 4 × 4 magic square in which the sum of each row, column, and diagonal is 2016.
1. Find a string of two or more consecutive integers for which the sum is 2016. How many such strings exist?
1. What is the value of the following series? $\frac{1}{1} \times \frac{1}{2} + \frac{1}{2} \times \frac{1}{3} + \frac{1}{3} \times \frac{1}{4} + \frac{1}{4} \times \frac{1}{5} + \cdots + \frac{1}{2015} \times \frac{1}{2016}$

1. What is the units digit of 22016?
1. 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?
1. What is the value of the following expression, if x + 1/x = 2? $x^\mathbf{2016} + \frac{1}{x^\mathbf{2016}} + \mathbf{2016}$

1. 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?
1. 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.)
1. 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?
1. 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: $\binom{n}{2} = 2016$

• What is the binary representation of 2016?
• What is the base-4 representation of 2016?
• What is the base-8 representation of 2016?