## Archive for January, 2016

### Snowzilla Math for Back to School

I don’t know where you live, or how much snow you’ve gotten, or whether your kids have been out of school for multiple days. But here in Falls Church, VA, it’s Thursday, January 28 — five full days after snow stopped falling from Winter Storm Jonas — and our schools are **still** closed.

My sons lounge around in their pajamas all day, only getting off the couch to interrupt my work-from-home day and ask for macaroni and cheese. It’s starting to feel like we’ve had two eight-year-old brothers-in-law take up residence.

That’s why I’ve used data from Snowzilla to create a series of math activities. Today’s assignment is for them to complete the following and not bother me till they’re done. Feel free to use any of these with the youngsters in your life, whether they’re your biological offspring from whom you need a break at home or your charges in a classroom who might enjoy the challenge.

What do geometry teachers do in a blizzard?

Make snow angles.Schools have had a record number of snow days. At this rate, the only math kids are doing is how many glasses of wine their mom drinks before 2 p.m. – Jimmy Fallon

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**1.** Chris Christopher, a macroeconomist at IHS Global Insight, estimated that Jonas’s economic impact would be somewhere between $500 million and $1 billion.

**a.** Write both of those numbers in the form 2^{m} × 5^{n}.

**b.** If all values within the range are equally likely, what is the probability that the impact will be greater than $800 million?

**c.** If all values within the range are normally distributed, what is the probability that the impact will be greater than $800 million?

**Bonus.** Can you think of another occupation where it’s appropriate to state a prediction in which the upper end of the range is double the lower end?

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**2.** In the Washington, DC, area, the average weekly sales in a typical supermarket is about $10 per square foot. In the two days leading up to Jonas, traffic to brick-and-mortar stores was 7.5 percent higher than usual. The graph below, based on national averages, shows the percent of weekly shoppers at grocery stores each day of the week.

Putting all this information together, as well any other data that you can find online, draw a graph that approximates sales at a typical grocery store in Washington, DC, for the month of January.

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**3.** Virginia Governor Terry McAuliffe estimated that snow removal costs the commonwealth $2 million to $3 million per hour. Estimate the total cost for Virginia to clean up Jonas’s mess.

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**4.** According to City Comptroller Scott Stringer, the cost of snow removal in New York City is approximately $1.8 million per inch. Estimate the total cost for New York City to remove the snow from Jonas.

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**5.** The estimate above is an average for 2003 to 2014. The two graphs below show the snowfall totals and snow removal costs for those 12 years. Which years had the highest and lowest cost-per-inch? (Click each image to enlarge.)

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### 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?