3 ms·
> You have to go out of your way (or get very unlucky if you're choosing random parameters) to construct an exercise that will fool a large portion of people.
by rcoveson 3y ago
> You have to go out of your way (or get very unlucky if you're choosing random parameters) to construct an exercise that will fool a large portion of people.
That's not remotely true. You're generally picking small integers, here, and frequently dealing with problems that have very few parameters.
"Species of birds in the genus Madeupicus all have the same proportions. Adult birds of one species in the genus have a wingspan of one meter and weigh one kilogram. How much do birds of a species in the genus with a two meter wingspan weigh?"
This is a very similar problem to the one in the original example. It has the same trick, which is that the integers on either side of the equation are the same in the first example, but they will not be the same in the second equation due to dimensional scaling.
Students do hundreds of math problems per week. Randomly-selected small integers will collide frequently.
And that's all ignoring the benefits of surprising people, which you still tacitly deny. What are you optimizing your questions for, "fairness"? "Predictability"? That sounds like a great way to ensure as many people as possible who didn't actually understand the subject matter will pass your tests.