Here's a third puzzle that I found in a book, slightly paraphrased because I don't entirely remember the format of the original.
A medical researcher is trying to test the effect of a certain drug on mice. He is supposed to collect data for all doses from 1 to 50 units, but only has the data collection resources for 25 tests. He has decided to only test dose amounts that are not multiples or factors of each other (for example, if he decided to use a dose of 15 units for a specific test, that would preclude tests for 1, 3, 5, 30, or 45 units). Moreover, because the drug is relatively expensive, he wants to use as little of the drug as he can manage to run these tests.
How can he arrange the dosage amounts so that he ends up using all 25 test packages, and the total units of dosage used in the tests are as low as possible?
The book had the answer, but one, it didn't explain how the answer was arrived at, and two, I don't remember what the answer was and no longer have that book with me.