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"Hat" Riddles - Next 10 of 3419.

Riddle: Sal I run. What is the anagrammed word?
Answer: Insular.
Riddle: What do you call a person who crosses the road twice without taking a shower?
Answer: A dirty double crosser.
Riddle: In wealth I abound; in water I stand; as a fencer I'm valued all over the land; at Venice I'm famous; by farmers I'm prized; respected by law, yet huntsmen despised; consternation and ruin ensue when I break; And the beasts of the forest advantage won't take. What am I?
Answer: I'm a bank.
Riddle: I help you hear, I am tiny as a dime, There are many versions of me. What am I?
Answer: A Hearing Aid!
Riddle: We first appeared outside in the early 1940s during World War II. Our construction was a simple mixture of glass and aluminum, with a flexible entrance that kept out unwanted intrusions. We were not migratory and never slept -- even at nighttime. The famous movie director, Alfred Hitchcock, once used one of us in his movie "The Birds" back in 1963, which resulted in some shattered glass. A famous "lady" once described us as being, "like a lighthouse on the highway", as we were easily seen at nighttime. In the year 2000, there were more than two million of us in existence, but as of 2020, our numbers have quickly declined, and there are now fewer than 100,000 of us remaining in the United States. We were greatly honored in 2015 when someone nominated us for inclusion into the National Register of Historic Places in the state of Arkansas. Who/what are we?
Answer: We are telephone booths.
Riddle: On the outside, beige walls surround a castle of the purest white, and a tressure of liquid gold hides in the center. What is it?
Answer: An Egg.
Riddle: I have heard of a something-or-other, growing in its nook, swelling and rising, pushing up its covering. Upon that boneless thing a cocky-minded young woman took a grip with her hands; with her apron a lord's daughter covered the tumescent thing. What is it?
Answer: Dough turning into bread.
Riddle: The more of me you put on, the more you can remove. I come in many forms, but I'm generally liquid up high and solid down below. If you avoid me, I won't care, but others will. What am I?
Answer: Soap.
Riddle: A wife called to her husband from the front door of their home stating, "Don't forget to raise the flag, but please don't be goofy and salute it afterward." Her husband responded by saying, "Don't you love your country?" The wife replied, "I am very patriotic, but I would never salute that flag. You embarrass yourself when you do it, especially when the neighbors see you." "Well, all I know is if I don't raise the flag, we'll lose our electricity, our car will be towed away, and eventually we will be evicted! Being a veteran of the Army, as long as the flag is red, white, and blue, I will always salute it!" "Oh, have it your own way, answered his wife, "but it's not the raising of the flag to which I object, it's you're saluting it afterward that bothers me!" What were the circumstances behind this couple's bizarre-sounding argument?
Answer: The flag on the couple’s mailbox in front of their home was painted red, white, and blue to resemble the American flag. When the husband put their outgoing bills and other mail in the mailbox, he had to raise the flag to be sure their outgoing mail would be picked up by their mail delivery person. Being a veteran and a patriotic person, he felt compelled to salute the flag each time he raised it.
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.)