What new things do you expect after solving a quadratic equation?
Omega places a series of 50 boxes in front of you, labelled numerically. Two of them contain explosive boobytraps while each of the remaining 48 contain $200,000. The sum of the labels on the trapped boxes is 55 while the product is 714. Which boxes would you not choose to open?
Nice example. To follow up:
Next, Omega places two boxes in front of you. One carries the label "The label on the other box contains a true sentence". The label on the other box reads "The label on the other box contains a false sentence". You are told that the box(es) without false labels contain $1,000,000, whereas the box(es) with false labels are boobytrapped. It is conceivable that the labels are meaningless - therefore not false. It is also conceivable that the labels are both true and false - contradictory, but paraconsistent.
Do you open the boxes?
Quadratic equations are relatively clear-cut.
Graham Priest discusses The Liar's Paradox for a NY Times blog. It seems that one way of solving the Liar's Paradox is defining dialethei, a true contradiction. Less Wrong, can you do what modern philosophers have failed to do and solve or successfully dissolve the Liar's Paradox? This doesn't seem nearly as hard as solving free will.
This post is a practice problem for what may become a sequence on unsolved problems in philosophy.