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 and , respectively. The “teaser” statement gives us
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?