January 2019 – Denise Gaskins' Let's Play Math

Stopping By Woods On A Snowy Evening

Whose woods these are I think I know.
His house is in the village, though;
He will not see me stopping here
To watch his woods fill up with snow.

My little horse must think it queer
To stop without a farmhouse near
Between the woods and frozen lake
The darkest evening of the year.

He gives his harness bells a shake
To ask if there is some mistake.
The only other sound’s the sweep
Of easy wind and downy flake.

The woods are lovely, dark and deep,
But I have promises to keep,
And miles to go before I sleep,
And miles to go before I sleep.

—Robert Frost

[And Why the Public Domain Matters.]

CREDITS: “Snow falling in a forest” photo (top) by Annie Spratt via Flickr (CC BY 2.0).

Happy 2019! Have you set any goals for the year?

My goals are to continue playing with math (1) in my homeschool co–op classes and (2) on this blog — and (3) hopefully to publish a couple of new books as well.

My favorite way to celebrate any new year is by playing the Year Game. It’s a prime opportunity for players of all ages to fulfill the two most popular New Year’s Resolutions: spending more time with family and friends, and getting more exercise.

So grab a partner, slip into your workout clothes, and pump up those mental muscles!

Rules of the Game

Use the digits in the year 2019 to write mathematical expressions for the counting numbers 1 through 100. The goal is adjustable: Young children can start with looking for 1-10, middle grades with 1-25.

You must use all four digits. You may not use any other numbers.

Solutions that keep the year digits in 2-0-1-9 order are preferred, but not required.

You may use +, -, x, ÷, sqrt (square root), ^ (raise to a power), ! (factorial), and parentheses, brackets, or other grouping symbols.

You may use a decimal point to create numbers such as .2, .02, etc., but you cannot write 0.02 because we only have one zero in this year’s number.

You may create multi-digit numbers such as 10 or 201 or .01, but we prefer solutions that avoid them.

My Special Variations on the Rules

You MAY use the overhead-bar (vinculum), dots, or brackets to mark a repeating decimal. But students and teachers beware: you can’t submit answers with repeating decimals to Math Forum.

You may NOT use a double factorial, n!! = the product of all integers from 1 to n that have the same parity (odd or even) as n. The Math Forum allows them, but I feel much more creative when I can wrangle a solution without invoking them.

For many years mathematicians, scientists, engineers and others interested in mathematics have played “year games” via e-mail and in newsgroups. We don’t always know whether it is possible to write expressions for all the numbers from 1 to 100 using only the digits in the current year, but it is fun to try to see how many you can find.

— Math Forum Year Game Site