UPDATE: (4:54pm, November 6, 2006) Here’s the letter I sent: Letter to Pizza Hut.pdf

No, I am not really calling for a boycott of Pizza Hut, but it was an eye catching title, wasn’t it? My family went to eat at Pizza Hut today and while we were waiting for my favorite pizza (thin and crispy, meat lovers), Emily and I were playing Tic-Tac-Toe on their kid’s placement. I do appreciate restaurants that provide a means to keep the kids preoccupied until the meal gets to the table. However, just across the page was a series of “Teasers”, one of which read

Inside a gum ball machine with red, yellow and blue gum balls, all but four are red and all but four are blue. How many gum balls are in the machine all together?

Being Saturday and having turned my brain off for a little R & R, it took me a little while to determine the fact that the question is not well-defined. After determining my solution set, I turned the placemat upside down and was disappointed to read their answer. It read,

Six (two red, two blue, two yellow)

So what’s wrong with that?

Well, it is true that their answer is a correct one, but as I mentioned the question is ambiguous. It is possible that the solution be a total of anywhere from 4 to 8 gumballs.

4 Gumballs: 4 yellow, 0 red, 0 blue

5 Gumballs: 3 yellow, 1 red, 1 blue

6 Gumballs: 2 yellow, 2 red, 2 blue

7 Gumballs: 1 yellow, 3 red, 3 blue

8 Gumballs: 0 yellow, 4 red, 4 blue

Of course, if you read the statement and believe it to say the machine must have at least one of each color, then the case of 4 gumballs and the case of 8 gumballs are eliminated. Nevertheless, that still leaves us with 3 different answers and their answer leads the kids to believe that because that one is right, it is the only right answer. Tsk, Tsk, Tsk.

I told you my brain was turned off so instead of simply recognizing the answers by simple logic, I had to set up a linear system to solve. Then, I determined that the linear system was underdetermined and dependent. Letting the number of red, blue and yellow gumballs be represented by [tex]r, b[/tex] and [tex]y[/tex], respectively. The “teaser” statement gives us

[tex]\left\{ \begin{array}{l}b+y=4\\ r+y=4 \end{array} \right.[/tex]

We assume the additional constraint on the variables to be positive integers. This leaves us with only the solutions above.

So, should I write a strongly worded letter to the Pizza Hut headquarters, or just let it go?

We are running out of places we can eat in this town. I say we let this one slide.

Don’t mess Pizza with hut. Just enjoy there pizza

Write them and say, “Thanks for putting a math question on the placemat — but here’s the problem with it…” At least PH is *trying* to include some numeracy in their kid stuff.

Let ‘em have it!

Definitely write and let them know the error of their way…

I’m crafting the letter now and will post it here so you can know just how merciless I was. (*wink wink)

Giggle, giggle. That’s my boy!

I was just glad I got the answer of 6 until you pointed out that there were other possible answers. then I didn’t feel so smart. However, I did think about the possibilities of your answers for 4 and 8 gumballs, but the question definitely states that there are three colored gumballs, so those woulnd’t work.

However, I am already semi-boycotting pizza hut. Everytime I call to order carryout, they screw things up. So, a couple of years ago, I told my wife that if she wanted pizza hut,she had to deal with the people.

I say write them! Simply because they might send you a real coupon (not like those that make you think you’re getting a great deal).

Speaking of Pizza, did you know it cost only $50k to start up a PapaJohn’s franchise?