Would be interesting to know if this is correct.<p><i>Please prove that the following problem is NP-hard, as if you were explaining it to a 5th grader. [...]<p>Pivot Scheduling is NP-hard, which means that it's really hard to solve. Imagine that you have a bunch of jobs, and you want to put them into two piles. You know that for each job, you can't put both parts in the same pile. In addition, you know that for some of the jobs, one of them must be put in a particular pile. To solve this problem, you have to try out all the different ways of putting the jobs into the two piles, and check whether they satisfy the constraints. And since there are so many different ways to try out, it would take forever to check all of them, so that's why this problem is NP-hard.</i>
I mean, why shouldn't we trust it?<p><i>Assume that R and I are both non-empty sets.<p>By the Axiom of Extensionality, for any two sets X and Y, if X and Y have the same elements, then X=Y. Therefore, if R and I have at least one element in common, then R = I.<p>Now, let r be an element of R and i be an element of I.<p>Since R and I are both non-empty sets, r and i must both exist in either set. Therefore, r = i, and thus R = I.<p>Therefore, the existence of rice pudding and income tax is established. QED.</i>