## Posts tagged ‘expression’

### My Wife’s Son

I’m fortunate to have Joshua Zucker as a friend and colleague. Knowing that my sons have a penchant for math, he recently sent me a set of *Got It!* cards. *Got It!* is a game in which number cards and operation cards are alternately laid out in a grid, and the object is to find a set of at least five cards (three number cards and two operation cards) that form an expression equal to a certain target number. If you find such an expression, the target card is added to your collection, and the person who collects the most target cards wins.

For instance, the grid below shows an arrangement of 36 orange cards that are to be used to form either 23 or 29 (the blue target card on the left). I’ll give you a moment to find such an expression yourself.

Tonight before dinner, my sons and I played *Got It!* for the first time, and the challenge above was one with which we were presented. In less than 10 seconds, Alex found an expression equal to 23. Starting with the 8 in the third row, first column, he constructed the following:

(8 + 3 – 1) × 2 + 3 = 23

As he explained his solution, he said, “Well, 8 + 3 – 1 is 10, times 2 is 20, plus 3… *simple*.” Part of me thought, “That’s pretty good.” But most of me thought, “Wow, did my six-year-old son really just best me in a math game and then declare that it was simple?” Sure enough, he had.

Apparently, that wasn’t sufficient, though. The next target card was 25, and Alex again found a correct expression faster than Eli or I. Eli tried to hand the target card to Alex, but Alex demurred. “No,” he said. “I’m not playing this round, so you and Daddy can get some cards.” Part of me thinks he’s just a sweet six-year-old who doesn’t want to trounce us… but most of me thinks he’s developing an attitude that needs to be nipped in the bud.

My only solace is that he’s *my wife’s son*, and I’m sure he didn’t get this from me.

This reminds me of a story.

A friend’s six-year-old son said, “Daddy, I need help with a math problem I couldn’t do at school today.”

“Sure”, the father says with a smile. “What’s the problem?”

“Well, it’s really hard. There are four ducks in a pond, and two more ducks come and join them. How many ducks are now in the pond?”

The friend stares at his son and says, “You couldn’t do that? You don’t know that 4 + 2 = 6?”

“Of course I know that,” he says. “But what’s that got to do with ducks?”

### A New Tattoo

I was both nervous and excited when I walked into the tattoo shop. I had been working extra hours in the tutoring center to save for this, and the moment had finally arrived. Sure, I could have played it safe and asked for a tribal pattern on my upper arm. But I’ve always lived by the mantra, “Go big, or go home.”

“What are we doing today?” the tattooist asked.

“How about *x* + 6 across my left cheek?” A blank stare. “You know, like from algebra,” I explained.

I got the sense he wanted to ask some follow-up questions… but then decided against it. Instead, he started inking. Twenty minutes later, he held up a mirror so I could see his handiwork.

“You don’t like it, do you?” he asked.

“No, no, I love it!” I said. “What makes you think I don’t like it?”

“I can tell by the expression on your face.”

### Depressing Expressions

Did you hear that Monday, January 23, 2012, was the most depressing day of the year? That’s according to Cliff Arnall, a British life coach who, for a little while, was a tutor at Cardiff University. He used the following formula to make his prediction:

In that expression, *W* = weather, *D* = debt, *d* = days until next payday, *T* = time since Christmas, *Q* = time since a failed quit attempt (such as abandoning a New Year’s resolution), *M* = motivation level, and *N _{a}* = need to take action.

When I heard that a psychologist was creating mathematical expressions, I had just one thought:

Why did the psychologist send the expression to a doctor?

Because he wasn’t being rational.

When I read the formula, my first thought was, “Wow, that’s an incredible bunch of rubbish!” (Funny, I don’t normally use the word *rubbish*. Maybe it happened because I read about the expression in a British newspaper?) Only *W* and *T* are universally measurable variables. While *D*, *d*, and *Q* are also measurable, they vary from person to person and shouldn’t be used to predict a global most depressing day. And what’s this nonsense about time from Christmas? Is that really a factor for Jews, Sikhs, and other non-Christians? (Note: Many online sources incorrectly state that *d* = monthly salary. But that would cause the formula to make even less sense.)

This expression has been used for several years to predict the most depressing day, and a similar expression has been used to predict the happiest day of the year. The happiest day expression, which is similarly unintelligible, regularly predicts a date in June. Interestingly, the “research” was sponsored by Wall’s Ice Cream. (Hmm, now why would an ice cream company have an interest in people being happy during the summer?)

It’s a little too early in the year to say that January 23 will be the most depressing day of 2012. In fact, January 23 isn’t even the most depressing day *so far* in January — that distinction belongs to Sunday, January 8.

As for crazy expressions, the following equation contains my favorite:

The value of *k* doesn’t matter, but the equation doesn’t hold if the placeholder variable *k* is not included.

Incidentally, this equation is related to the following problem: Raise *n* + 1 consecutive integers to the power *n*. Subtract the first from the second, the second from the third, and so on, until you’re left with a set of *n* integers. Then subtract the first from the second, the second from the third, and so on, until you’re left with a set of *n* ‑ 1 integers. Continue this process until you’re left with just one integer. Its value may surprise you.

### Welcome to 2011

An original problem to kick off the new year:

Place three operators (+, –, ×, ÷) between the digits below to make an expression equal to 2011.

1 2 3 4 5 6 7

For instance, using three + signs, you could make the expression 123 + 45 + 6 + 7, which is equal to 181.

A more standard problem to begin any new year is this:

Combine the digits of the year (in this case, 2, 0, 1, 1) to create each of the numbers 1–100. Extra credit if you can keep the digits in the same order as they appear in the year. For instance, 2

^{0}– 1 + 1 = 1 would be a way to make 1 with the digits in order, and 10 – 2 + 1 = 9 would be a way to make 9 with the digits out of order.

I hope that 2011 brings you peace, love, happiness, and lots of problems!