Answer to the last riddle: Separate the pile into two piles of 13 and 39, both with an unknown number of faceup cards. Now flip over the pile of 13. You now have the same number of faceup cards in both piles.
Didn't know what to make of that one eh? Hm. I had a hard time believing it too, had to try it out for myself. In fact, you can prove it algebraically (a cookie for whoever can show me this proof in the comments!)
Consider two identical cups, one half-full of tea, the other half-full of milk. You take a teaspoon of milk from the milk cup and put it in the tea cup. Then you take a spoonful out of the tea cup and put it in the milk cup. You take another spoonful out of the milk cup and into the tea cup, and one final spoonful from the tea cup to the milk cup. Now: is there more tea in the milk cup, or more milk in the tea cup?