Heh heh heh. I'm flattered, but really, all it takes is for one kid to come up with one strategy that works; after that, others could find out about it through word of mouth or the internet. I could imagine a kid noticing by accident that... not having access to the calculator, I can't be sure whether any specific example will work, other than the ones described on the website... but I can imagine a kid finding by accident that, while "A * B * C" fits a certain estimate, if you ask the calculator what A * B is (about 20) and put in "20 * C" and give the same estimate, it will reject it. It's likely that either he will figure some things out (trying things like putting (A * B / 20) * C, and trying that with other values of C), or he will be confused and announce it to the class, in which case someone else will probably figure things out. And this is to say nothing of a clever kid who knows math and who deliberately looks in the first place for ways to defeat the device (perhaps after the device offends him by rejecting an honest estimate).

I would warn in general against underestimating the cleverness of children, even those who appear not to understand the material of the class. From John Holt's "How Children Fail" (letter from May 10, 1958), describing some elementary school classes:

Children are often quite frank about the strategies they use to get answers out of a teacher. I once observed a class in which the teacher was testing her students on parts of speech. On the blackboard she had three columns, headed Noun, Adjective, and Verb. As she gave each word, she called on a child and asked in which column the word belonged.

Like most teachers, she hadn't thought enough about what she was doing to realize, first, that many of the words given could fit into more than one column and, second, that it is often the way a word is used that determines what part of speech it is.

There was a good deal of the tried-and-true strategy of guess-and-look, in which you start to say a word, all the while scrutinizing the teacher's face to see whether you are on the right track or not. With most teachers, no further strategies are needed.

This one was more poker-faced than most, so guess-and-look wasn't working very well. Still, the percentage of hits was remarkably high, especially since it was clear to me from the way the children were talking and acting that they hadn't a notion of what nouns, adjectives, and verbs were. Finally one child said, "Miss —, you shouldn't point to the answer each time." The teacher was surprised, and asked what she meant. The child said, "Well, you don't exactly point, but you kind of stand next to the answer." This was no clearer, since the teacher had been standing still. But after a while, as the class went on, I thought I saw what the girl meant. Since the teacher wrote each word down in its proper column, she was, in a way, getting herself ready to write, pointing herself at the place where she would soon be writing. From the angle of her body to the blackboard the children picked up a subtle clue to the correct answer.

This was not all. At the end of every third word, her three columns came out even, that is, there were an equal number of nouns, adjectives, and verbs. This meant that when she started off a new row, you had one chance in three of getting the right answer by a blind guess; but for the next word, you had one chance in two, and the last word was a dead giveaway to the lucky student who was asked it. Hardly any missed this opportunity, in fact, they answered so quickly that the teacher (brighter than most) caught on to their system and began keeping her columns uneven, making the strategist's job a bit harder.

He adds later:

Not long after the book came out I found myself being driven to a meeting by a professor of electrical engineering in the graduate school of MIT. He said that after reading the book he realized that his graduate students were using on him, and had used for the ten years and more he had been teaching there, all the evasive strategies I described in the book—mumble, guess-and-look, take a wild guess and see what happens, get the teacher to answer his own questions, etc.

But as I later realized, these are the games that all humans play when others are sitting in judgment on them.