## Archive for December 19, 2015

### Math Problems for 2016

“What homework do you have to do tonight?”

I ask my sons this question daily, when I’m trying to determine if they’ll need to spend the evening doing word study or completing a math worksheet, or if we’ll instead be able to waste our time watching The Muppets or, perhaps, pulling up the animated version of Bob and Doug Mackenzie’s *12 Days of Christmas* on Dailymotion.

When I asked this question last night, though, the answer was surprising:

We have to do our reading, but we already completed

yourmath problem.

*My* problem? I had no idea what this meant. So they explained:

It’s not a problem you gave us. It’s one we got from [our teacher], and it says, “This problem was written by Patrick Vennebush.”

I was puzzled, but then it dawned on me. I asked, “Does it have a monkey at the top with the word *BrainTEASERS*?”

“Yes!”

“Which problem?”

“It’s about the word CAT.”

I knew the problem immediately. It’s the Product Value 60 brainteaser from Illuminations:

Assign each letter a value equal to its position in the alphabet (A = 1, B = 2, C = 3, …). Then find the product value of a word by multiplying the values together. For example, CAT has a product value of 60, because C = 3, A = 1, T = 20, and 3 × 1 × 20 = 60.

How many other words can you find with a product value of 60?

As it turns out, there are 14 other words with a product value of 60. Don’t feel bad if you can’t find them all; while they’re all allowed in Scrabble™, the average person won’t recognize half of them.

You can see the full list and some definitions in this problem and solution PDF.

This problem resurfaced at the perfect time.

With 2016 just around the corner, no doubt many math teachers will present the following problem to students after winter break:

Find a mathematical expression for every whole number from 0 to 100, using only common mathematical symbols and the digits 2, 0, 1, and 6. (No other digits are allowed.)

And that’s not a bad problem. It gets even better if you require the digits to be used in order. For instance, you could make:

**2**= 2^{0}+ 1^{6}**9**= 2 + 0 + 1 + 6**36**= (2 + 0 + 1)! × 6

But that problem is a bit played out. I’ve seen it used in classrooms every year since… well, since I used it in my classroom in 1995.

So here are two versions of a problem — the first one being for younger folks — using the year and based on the Product Value 60 problem above:

How many words can you find with a product value of 16?

How many words can you find with a product value of 2016?

There are 5 words that have a product value of 16 and 12 words that have a product value of 2016 (**spoiler**: those links will take you to images of the answers). As above, you may not recognize all of the words on those lists, but some will definitely be familiar.