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Riddle:
One summer evening, as Irene sat on the front porch of her old Kentucky home, she witnessed about a dozen men in two large trucks pull up to an old abandoned farmhouse about a hundred yards from hers. Suspicious, she grabbed her binoculars and observed two of the men approach the old farmhouse --- and set it on fire! After ten minutes had passed, the farmhouse was completely engulfed in flames, but neither Irene nor any of her neighbors in sight of the burning building ever bothered to call 9-1-1 to report any of these events. To make matters even worse, two police cars passed the flaming house but never bothered to stop. What happened to civic duty and responsibility? Has society totally turned its back on the idea of neighbors helping neighbors; or is there an alternate explanation for these events? What exactly was happening here?
Answer: As Irene and her neighbors looked out of their respective windows, they all saw the two large trucks were actually fire engines carrying about a dozen firemen. They obviously had come with permission from the owner of the abandoned farmhouse, to perform a training exercise on fire fighting techniques (Irene and her neighbors had received notification from the fire company of this planned exercise earlier that same week). After the firemen started the building on fire, they proceeded to practice their skills in putting out the blaze. The police cars who passed the fire saw the firefighters were training, as they also had been notified of this planned fire at the start of their shift. The owner of the building got rid of his old farmhouse, and gave the fire company some needed practice, providing a win-win situation.
Riddle:
He's a boastful, puffed-up fellow, wearing spurs; eyes gleaming yellow. As he proudly struts about, he's in charge, there is no doubt.
What is he?
Riddle:
You have 52 playing cards, 26 red, and 26 black. You draw cards one by one. A red card pays you a dollar. A black one fines you a dollar. You can stop any time you want. Cards are not returned to the deck after being drawn. What is the optimal stopping rule in terms of maximizing your expected payoff? Also, what is the expected payoff following this optimal rule?
Answer: The solution to this problem is, in my opinion the most difficult to understand of all the puzzles. Indeed I was unable to solve it and didn't receive a complete solution until two years after originally posting it. The final solution, in the form of the spreadsheet was sent to me by Han Zheng. For this reason I have left on the page the thoughts i had before I had the final solution as they represent an easier to understand and more simplistic approach. Also the reasoning may help you arrive at the final solution by yourself or help you understand it. I would recommend reading that answer before you dive into the full answer. But an important thing to note are that as the player we can't lose this game as we can gamble till all the cards are drawn and our net position is zero. From our earlier analysis it is clear we need a dynamic quit rule. A singal value is not sufficent. We must, at each stage consider what cards are remaining, and therefor the probability of a positive or negative outcome from drawing again. For the explanation i will ask you first to consider a deck containing only 6 cards, 3 +ve & 3 -ve (note i'm no longer calling the cards black and red, it confuses me.)
Riddle:
I'm greater than God, yet worse than the devil. I am what the miser spends and the spendthrift saves. I am what the blind see and the paralised hold. What am I?
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