The Famous Hole in a Sphere
I don't think that's true. The question is asking what the remaining volume of the solid sphere is after the cylinder is removed. Also, check out this picture. Notice that the height h of the cylinder does not equal the diameter of the sphere. context 
3 Coins
The key is to infer the probability that each coin was selected based on the (heads,heads) outcome for the first two flips. Label the three coins:
Data = HH. In general, as per Bayes' Rule, P(Ci  Data) is proportional to P(Data  Ci)*P(Ci), so:
Now, P(H  Data) = sum over Ci ( P(H  Ci) * P(Ci  Data ) = 0 * 0 + (1/2) * (1/5) + 1 * (4/5) = 9/10. In summary, probability of heads on the third flip (given the first two flips being HH) is 9/10. context 
All the King's Wine
I would first try to find out if the poison isn't colorless, and if that's the case, you could inspect the color of each wine. It would be especially obvious if it's white wine. context 
All the King's Wine
Can you elaborate on your solution? context 
All the King's Wine
That's hilarious! And why is the solution you were clearly driving me towards one which takes advantage of an undocumented and unreliable epiphenomenon? Does your team usually write code whose correctness relies upon undocumented and unreliable correlations, correlations whose magnitudes can vary widely as a result of implementation details? context 
All the King's Wine
You're right. Perhaps the original intention was to say "each of the servants can/must try multiple wines"? context 
All the King's Wine
I was asked this question in a job interview last year. It's a great question that really challenges one's ability to dissect a problem and carefully use the given information. (I'm being intentionally vague so I don't ruin it for others) context 
Age of Three Kids
Solid puzzle. context 
Don't Mate in One
A picture has been added for clarity. context 
Sand Timer Puzzle
Sakshi  no spamming. context 
1978
+1 to Ryan Miller's comment. context 
Gold or silver?
I guess this one falls more into the "riddle" category than "chemistry". context 
3 Coins
What's your reasoning alvinfromva? context 
The Female Star
Most of the puzzles with the "word puzzle" tag may be specific to the English language, but most of the other puzzles are languageindependent. context 
No if() Only abs()
That's a good point. More verbosely, {a+b+abs(ab)} / [{a+b+abs(ab)}+{a+b+abs(ab)}] context 
1978
Spoiler tags were recently implemented so that you can ^{ spoiler}hide parts of your comments! context 
Electrical Deaths
I agree. There's quite a few loopholes in the solution, but it's a fun problem nonetheless. context 
Balloon in an Elevator
In the confines of an elevator shaft where the area of the base of the elevator covers most of the crosssectional area of the shaft, I would imagine the elevator would reach terminal velocity quite quickly and stop accelerating at G, at which point the balloon would go up. So I guess your answer is assuming an ideal case where the lift keeps accelerating at G? context 
Balloon in an Elevator
When the lift is in freefall, wouldn't it become weightless and therefore its contents would also become weightless? I would think that this would make the balloon drop towards the floor of the elevator. What's your reasoning Timmmm? context 
The Cabin
That's a great point. We're always brainstorming new features so we'll definitely keep this in mind! context 
The Sinking Island
Most of the puzzles on here have solutions. Click Show Answer and Show Solution. context 
12 Identical Balls
I agree. I assume it means "identical in appearance". context 
Gold or silver?
If you go down the path of differentiating weight vs mass, you would have to assume that gravity is the same when weighing both elements. context 
Gold or silver?
Touché. Clever observation. context 
Ball Drop
I agree. I'll assume the golf ball would encounter less drag, and would therefore hit the sea floor first. context 
Survivor
I knew it looked familiar! context 
Crazy Google Interview Question
Interesting approach! To be fair, if you were the size of a nickel, your shoe laces wouldn't be long enough to wrap around the rotating assembly (unless you had abnormally long shoe laces). context 
Sum of Two Prime Numbers
There's a Show Answer button below the puzzle! context 
Carpeting a Donut
I agree, that's a lot more intuitive than the OP's solution. context 
Bit Pair Swap
I don't think that works. For example, if you have 
Find the Missing Number
Not sure I follow. 7 4 8 3 9 7 6 5 10 ? 8 4 The first and last numbers in each column don't have the same number of letters: ("four","eight"), ("seven, "five")? Also, the question specifies that each row follows the same pattern of numbers. Can you provide an example of your solution? context 
Find the Missing Number
Ah, very clever solution! Have you heard this problem before or did you figure that out by observation? context 
Coin Flip
Wow, you even went as far as the Monte Carlo simulation. Impressive. context 
The doublesquare number problem
Nice, although brute forcing ruins all the fun! :) In general, the space of solutions to this problem lie on the circle defined by 100x+y = x^2 + y^2. Here it is on WolframAlpha. context 
Charlie and the Chocolate Factory
Urvesh, there's a Show Solution button to check if your solution is correct! context 
Multiples of 8 plus 1
Agreed, great solution! context 
The Bookworm
+1 (3 x 2.5")  0.25" for the front cover of Vol. 1  0.25" for the back cover of Vol. 3. context 
Swap Variables in Place without XOR
Yep, that's exactly the solution provided. context 
Tea and Wine
Hmm, that makes sense. I think the hardest part of this solution is intuitively understanding the duality between tea and wine proportions during the second transfer. context 
1978
Well played, good sir. context 
12 Identical Balls
There's also the 9 ball version with 2 weighs. context 
Tooth Paste, : Profit
I think the solution here rests on some assumptions that aren't clear in the question: * What does the mouth diameter have to do with the actual volume of toothpaste in the tube? Wouldn't this just be compensated for by just squeezing the toothpaste tube less or more? * Where is the 10, 2 and 3 days coming from? If I use 1g per day from the 100g toothpaste, it'll last me 100 days :) context 
Lab Rat on the Run
Can you elaborate on your solution? I'm not sure I understand your ^{ spoiler}(8+t) and (2+t) factors since t is expected time inclusive of any failed attempts. context 
Death by drawing?
Yeah, the math is a bit messy, but you're finding the max of this. I'm not sure how to treat the b and w variables as whole numbers in Wolfram Alpha, but under the assumption that w > 0, where w is the number of marbles in the first bag, you're answer of 73.7% makes sense. I think this should solve it, but free Wolfram Alpha is telling me I exceeded standard computation time and need to pay for more :(. context 
No if() Only abs()
That's an awesome explanation. MoralMachine, I suggest adding it to the puzzle solution. context 
7
5
Bug's Eye
You are a bug sitting in one corner of a cubic room. You wish to walk (not fly) to the extreme opposite corner – the corner furthest from you. Describe the shortest path that you can walk.

Doable

0
4
Cutting Numbers
When is Seven half of Twelve?

Easy

5
A Pharmacist's Nightmare
You have 5 jars of pills. Each pill weighs 10 gram, except for contaminated pills contained in one jar, where each pill weighs 9 gm. Given a scale, how could you tell which jar had the contaminated p
...

Hard

6
8
Cooking Time
A cook must put a souffle exactly 9 minutes at the oven, but he only have a 7 minutes hourglass and a 4 minutes hourglass.
How can he measure 9 minutes with those clocks?

Doable

1
3
Classic Knights & Knaves
Raymond Smullyan has made a career of writing logic problems. His most famous have to do with a mythical island of Knights and Knaves. Knights always tell the truth, and Knaves always lie.
As you a
...

Doable

7
3
Burning Rope
There are two lengths of rope.
Each one can burn in exactly one hour.
They are not necessarily of the same length or width as each other.
They also are not of uniform width (may be wider in middle th
...

Doable

7
4
Tea and Wine
You take a spoon of wine from a barrel of wine and put it into your cup of tea. Then you return a spoon of the (nonuniform) mixture of tea and wine from your cup and put it in the barrel. Now you ha
...

Doable

6
3
Grey Squares Illusion
Square A is the exact same shade of gray as square B.
It's true, check out the reconstruction.

Doable

9
10
The Monty Hall Problem
You’re on a game show, and you’re given the choice of three doors: Behind one door is a car and behind the other two doors are goats.
You pick a door, say No. 1, and the host, who knows what’s behind
...

Doable

10
2
Two Trains
Two trains (Train A and B) with 200 km between them are travelling towards each other at 100km/h. A mosquito, initially standing on the front of Train A, starts travelling towards Train B at 150km/h. O
...

Doable

45
11
The Sinking Island
You and 3 friends are on an island that is sinking. There is one bridge from the island to the mainland that supports at most 2 people at once. However, it's dark outside so anyone crossing the bridge
...

Doable

4
5
Electrical Deaths
You and your friend are driving out in the pouring rain one night. It soon becomes much to hard too see, so you stop at closest house possible. When you knock on the door, an old lady welcomes you to
...

Doable

10
2
Mutilated Chessboard Problem
Suppose a standard 8×8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares?

Hard

12
1
Choose the Next Letter
Choose the next letter in the sequence:
O T T F F S S ?

Doable

4
2
There are only 4 circles and none of them touch
Source: reddit.

Easy

2
3
Nice to meet you
At a secret meeting, everyone shakes hands exactly once with every other person present.
Altogether there are fortyfive handshakes. How many people attended the meeting?

Easy

6
9
Find the Missing Number
In this table, each row across follows the same pattern of numbers. See if you can discern the pattern and fill in the missing number in the bottom row.
7 4 8
3 9 7
6 5 10
?
...

Doable

1
1
Random Puzzle
Here’s something I heard from a friend, I thought it was appropriate.
What do you call a 4 foot tall fortune teller who is wanted by the law?
Good luck.

Hard

2
3
Marble Weights
You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in the middle. The device enables you to c
...

Hard

1
7
Parodoxical Statements from Life
Nobody goes to that restaurant; it’s too crowded.
Don’t go near the water ’til you have learned how to swim.
The man who wrote such a stupid sentence can not write at all.
If you get this messa
...

Doable

8
3
The Tallest Mountain
A man approaches you with a very enigmatic look on his face. He asks your for a bit of your time and if you could answer a quick question for him. He asks: “Before Mt. Everest was discovered, which w
...

Easy

13
15
Bit Pair Swap
In one line of C or Java, how would you swap every pair of bits in a byte? That is, swap bits 0 and 1, 2 and 3, 4 and 5, 6 and 7.
Example: 0110 1010 becomes 1001 0101.

Doable

5
1
3 Brilliant People
There are three genii standing in a row in a room facing the same direction. Thus, the genius at one end can see the two genii ahead of him, the genius in the middle can only see the one genius ahea
...

Doable

2
3
The North Pole Bear Puzzle Reloaded
A man walks 1 mile south, then 1 mile east, and finally 1 mile north to find himself in exactly the same position as he started. He is NOT at the north pole, nor does he shoot a bear.
Where is he?
...

Doable

2
2
The Number Problem
What does 3685=?
8809=6
7111=0
2172=0
6666=4
1111=0
3213=0
7662=2
8096=5
9312=1
4444=0
6824=3
9999=4
0345=1
2359=1
5522=0
9884=5
Enjoy, this is quite interesting.

Doable

5
9
The Stealing Mailman
This is a fairly simple problem that can cause some people trouble.
Kevin and Sophia want to mail high confidential letters between each other. They know that the mailman is crooked and opens the le
...

Doable

8
13
The Famous Hole in a Sphere
This incredible problem was first made famous by Martin Gardner with his ‘Mathematical Games’ column published in Scientific American throughout the 60s and 70s.
A cylindrical hole, 6 inches long,
...

Hard

1
3
3 Painted Ladies
There are 3 smart old ladies standing in a desert such a way that each lady can see the other two. Each of the 3 ladies has paint on her face. Seeing this, all three ladies begin laughing. After a wh
...

Doable

11
3
Measuring Up
You have a 3 and a 5 litre water container, each container has no markings except for that which gives you its total volume. You also have a running tap. You must use the containers and the tap in su
...

Easy
