27 12 Identical Balls 
54 All the King's Wine 
9 Unfair Coin 
10 3 Coins 
20 Odd Pills 
15 Swap Variables in Place without XOR 
17 Multiples of 8 plus 1 
7 Bug's Eye 
6 Partitioning a set 
5 Matchsticks 
54 

All the King's Wine 
10 

3 Coins 
17 

Multiples of 8 plus 1 
Carpeting a Donut
The cool thing in the 2nd solution is that it uses intuition about the question
It's an interesting way to look at problems in general...of course you can't always assume that what you think you see or don't see in the question is intentional. context 
Multiples of 8 plus 1
Ah too bad  you publish any of these, by chance? context 
Multiples of 8 plus 1
Fair enough  I'm an engineer...I know just enough math to be dangerously wrong sometimes. You might enjoy this one if you haven't seen it already. context 
Multiples of 8 plus 1
Very interesting proof. Are there any other patterns like this that exist among square (or nth powers in general)? context 
3 Coins
Good call applying Bayes' Theorem that way. My first thought was to use the HH information just to eliminate the alltails coin. I think your logic is valid. context 
12 Identical Balls
I've heard the variant of this where there's one ball that's heavier, but that's muuuch easier. context 
9
Unfair Coin
Say you have an unfair coin: a coin whose probability of flipping heads and flipping tails is unknown but nonzero.
Can you design a game where you and your opponent have an equal chance of winning?

Doable

10
20
3 Coins
Not sure what the answer is, ideas welcome!
You have 3 coins, one always comes up heads, the second always comes up tails, and the third is a fair coin. You select a coin at random. After selecting
...

Easy
