Math Puzzle Inventing – Can You Do It?

This is the 6th in the draft purge series. It was first drafted in May 2011. If you have examples of this type of math puzzle, please include them in the comments.

Since the first time I used email back in 1991, people have sent me various versions of the puzzle “I can guess your birth year.” The results end up as something like:

This year (and this won’t work for any other year)
Your phone number
Your birth date
Your favorite number and the year you were born
Your blood type

Okay, that’s exaggerating a little. But it seems like these puzzles get wilder and wilder.

When I receive these emails, it’s usually from a family member with the preface: “Can you tell me how this works?”

So I’ve dissected tons of these over the years. And I’ve always thought, “You know – I could totally make my own math puzzle like this!”

You can invent your own math puzzle!

The trick to this math puzzle is to add zero and multiply by one in clever ways.

First you pick the result you want. Like the last four digits from my childhood phone number: 4347.

Factor it into primes, if you can. Let your kids do this by hand if you want them to have practice on factoring. If they struggle, you or they can calculate the prime factors using an online service like this one.

Mine is: (3)(3)(3)(7)(23)

If you can’t factor into primes, subtract a single digit number and try it.

Like 4349 – it’s prime, so subtract 2 and then use that to do the rest of this.

At the end of the whole math game you’ll just need to put one more step that includes subtracting this number.

Start constructing the math game.

The starter line for your game will be “Choose a single digit number from 1 to 9.”

We’re going to construct our game using this, with x as the chosen digit.

Here’s how it will work. Let’s say they choose the number 8. It will look like this:

But we can’t just give them that.

We have to make it nifty. After all, a math game with very little math isn’t much of a math game.

Change some of the prime factors into addition or subtraction problems. And combine some of the smaller ones.

Instead of (3)(3)(3)(7)(23), we now have (7-4)(63)(20+3).

Keep on playing, calculating and being clever!

I’ve left off my playing here:

I’ll keep going until I have a nice set of instructions. Then I can do this on my Ma, Paps, my siblings and all my childhood friends that remember that phone number.

And it’s a great learning tool!

Kids will learn and practice order of operations and algebra. At the same time, they create something they can email or perpetrate on another person – preferably a grown up – and impress them!