REMINDERS: Answers in red.  Solvers (submitted/correct) in blue. (Forgive any omissions, but feel free to inform.) Comments in green. For further elaboration, please feel free to ask! 

1. (An old classic!)  Your unorganized sock drawer contains 18 white socks and 18 blue socks. How many times do you need to reach inside the drawer and take out a sock at random to guarantee you have a sock of each color? To be sure of a sock of each color, you’d have to pull out 19 socks.  Frank Green, Rita Barger, Jim Waterman, Amy Ragsdale
2. A cowboy rode into town on Friday. He stayed in town for three days and rode back out on Friday. How is this possible?  The horse’s name was Friday. 🙂  (Other alternate solutions here, including a perfectly-good-but-convoluted one from our ‘alternate solution master’ Jim Waterman.) Frank Green, Rita Barger, Jim Waterman, Jennifer Steele DeWeerdt, Amy Ragsdale
3. A palindrome is a number that reads the same forwards and backwards (like 202 or 454).  How many palindromes are there between 100 & 1000? 90.  Frank Green, Rita Barger, Jennifer Steele DeWeerdt, Amy Ragsdale
4. (A future hypothetical twist to a BT from last time)  The 52nd and 54th Presidents of the US have the same mother and father, but are not brothers and are not the same man.  How can this be? They are either brother/sister, or two sisters. Frank Green, Rita Barger, Jim Waterman, Jennifer Steele DeWeerdt, Amy Ragsdale
5. A woman was in her hotel room when there was a knock on the door. When she opened the door slightly, there was a man she’d never seen before.  He said, “I’m sorry, I have made a mistake, I thought this was my room” and walked away.  The woman went back into her room and phoned security.  Why was the woman so suspicious? No ‘official’ answer provided where I found this, but seems to me that if you’re going to your own room, you’d have a key and wouldn’t be knocking! Jennifer Steele DeWeerdt, Amy Ragsdale
6. a) How many ways are there to re-arrange the letters in the word ‘STOP’ ? 24 b) How many of those form a common-usage word? 6 (stop, spot, post, pots, tops, opts). Credit for 5 or 6 (OPTS is often omitted.) Frank Green, Rita Barger, Jennifer Steele DeWeerdt, Amy Ragsdale
7. Augustus De Morgan was a mathematician who lived in the 19^th century.  He once wrote, I was x years old in the year x².  a)  How old was he when he said that? Technically, he could have said it (past tense) in any year after 1849.  (See below).   B) What was his birth year?  1806 or 1807.  (43×43 = 1849, and it’s the only such year in the 1800s, so 1849 – 43 = 1806.)  Frank Green, Rita Barger, Amy Ragsdale
8. Several years ago, I drove a nail into a tree exactly five feet above the ground.  The tree grows at the rate of one half-foot a year.  Eleven years later, I returned to the tree.  How far above the ground was the nail? 5 feet.  (Trees grow from the top. :-))  Rita Barger, Jennifer Steele DeWeerdt
9. A man wanted to encrypt his password but he needed to do it in a way so that he could remember it. He had to use seven characters consisting of letters and numbers only (no symbols like ! or <). In order to remember it, he wrote down “You force heaven to be empty.” What is his password? U472BMT.   Amy Ragsdale (Partial credit to Frank Green for U4cH2BE.)
10. Guess the next three letters in the sequence:  GTNTL.ITS.  (GuessTheNextThree . . .) Frank Green
11. (Repeat) A digital clock forms palindromic times 114 times each day.  What is A) the least (2 min, between 9:59 and 10:01)  and B) the most amount of time between two palindromic clock numbers (1 hour, 10 min, twice, between 10:01 and 11:11 and then to 12:21)  Amy Ragsdale
12. (Ignore numbering snafu.  Can’t fix.)  Answer for #12 below:  They’re probably all stupid :-), but the most so is Boy #4, who will fall as a result of his own cutting.   Amy Ragsdale
13. 

BONUS1:  There are three light switches outside of a room:  #1, #2, and #3- They are connected to three light bulbs inside the room.  The door to the room is closed and you can’t see in. All three switches are currently off.  You need to figure out which switch belongs to which bulb. You can use the switches however you want to, but can only enter the room once. How do you do it?  Turn on Switch #1 (say) and leave on.  Turn on Switch #2 for ten minutes and then turn off.  Then go into room.  The bulb that is on belongs to Switch 1, the bulb that is warm belongs to Switch 2, and the other to # 3.  Frank Green.
BONUS 2: The Jan/Feb BTs mention Year Product Days  (For reminder, see Item 4 of this link.)  Are there any YPDs in each century with seven (7) or more YPDs?  xx24 each century has 7.  (1/24, 2/12, 3/8, 4/6, 6/4, 8/3, and 12/2.)  Frank Green.
BONUS 3:  A golf ball falls randomly onto a circular green 10 meters in radius, with the cup at the center.  What is the probability that the ball is within 1 meter of the cup?  Assuming A) the ‘falling’ is really random, and B) we’re talking ‘within 1 meter of the center of the cup’ (which, BTW, allows for a ‘hole in one’), then the answer is 1/100.  (Area of green = PI x 10 x 10 = 100(pi).  Area of inner circle = PI x 1 x 1 = (pi).)  Amy Ragsdale