165
votes
Accepted
Three voting prisoners
Another intuitive, no-math (and I believe best) strategy could be as follows:
This ensures that
The majority won't vote 1 (Steaks) when they would be wrong.
The majority will vote 1 the first night ...
- 1,466
112
votes
Accepted
100
votes
The Magic Money Machine
Yes, you should definitely accept the deal.
The puzzle clearly states that pushing a button labeled "Poof!" will remove a coin (emphasis mine) from box $i$, and cause two coins to magically appear in ...
- 13.4k
79
votes
Accepted
How to beat Count Dracula
The lockets and coffins are always found in loops.
open a coffin
look at the number of the locket in the coffin
go to the coffin with the same number as the locket
open the coffin
repeat from 2
At ...
- 5,856
62
votes
Accepted
60
votes
Accepted
Coin Flipping Game with the Devil
Satan should stick to fiddling. You will win, and here is a simple proof.
Consider the game $n$ turns at a time. After each cycle of $n$ turns, all the coins are in their original position (though ...
- 7,758
54
votes
Accepted
Deceptive dice game
You can make arbitrarily large sets of dice with this property.
Start with Efron's dice:
A: 4, 4, 4, 4, 0, 0
B: 3, 3, 3, 3, 3, 3
C: 6, 6, 2, 2, 2, 2
D: 5, 5, 5, 1, 1, 1
A beats B, B beats C, C ...
- 33.4k
52
votes
Accepted
50
votes
Accepted
50
votes
√2 without pressing √ on a Scientific Calculator
One possibility, if starting with an operation automatically prepends Ans:
Why does this work?
- 144k
49
votes
Accepted
Extreme Gerrymandering
The current president should choose the numbers
9($L$), 32($n_1$), 8($n_2$), 5($n_3$), 5($n_4$), 5($n_5$), 5($n_6$), 5($n_7$), 5($n_8$), 5($n_9$).
In the lowest sub-sub-...-subgroup, the president ...
- 11.7k
49
votes
Accepted
The Dwarves' Test
A dwarf with a red dot will
A dwarf with a blue dot will
Therefore, on the $N$th day, all dwarves with red dots are present, and all dwarves with blue dots are not.
- 33.4k
49
votes
Accepted
Pirate democracy at its finest
I have a hunch that the answer is
Explanation:
Continuing this way, we see that
- 27.4k
48
votes
Red and Blue in the Chocolate Fountain Room
The prisoners agree that:
Each prisoner with a blue nose will:
Each prisoner with a red nose will:
- 21.8k
48
votes
Accepted
Is there any easy way to solve this lock puzzle?
There is an easy way to solve it in the minimum number of moves.
The reason this works is:
- 47.7k
46
votes
Accepted
Can the Policeman catch the Thief?
Yes, the policeman can catch the thief, although it may take a very long time. In particular, the following strategy works: The policeman starts in the center. First, he makes a counterclockwise loop ...
- 7,801
45
votes
Accepted
Draw 4 straight lines to create 10 equal squares in this image
Please ignore my painting skill. i am not good at it
- 679
43
votes
Accepted
The Magic Money Machine
The answer, as I'm sure most people are guessing, is...
Here's my solution:
Also, I apologise for the formatting. I'm new to SE.
- 1,222
41
votes
Accepted
41
votes
Accepted
There are 2,001 doors leading to 2,001 hallways. How quickly can you find the way out?
Let's number the hallways (doors) from $1$ to $2001$ from west to east.
One important observation is that:
This is because:
Now, another important observation is that, if a dead-end room connects ...
- 33.9k
40
votes
Speak without using the letter "b"
You could count upwards from 1, because none of the numbers less than a billion contains the letter "b".
However, this might be repeating words if "101" is considered to contain "one". (The version I'...
- 33.4k
40
votes
Will a greedy algorithm solve Tatham's Flood?
It's definitely not optimal! Here's a counterexample:
Start from the white area.
Greedy algorithm would make you do all the colours on the top right (5 moves: yellow, green, dark green, blue, dark ...
- 11.9k
40
votes
How can one solve a Rubik's cube without relying on guides/algorithms?
There are three techniques that allow you to come up with useful move sequences for solving a cube.
Conjugation
This is where you already have a move sequence that does one thing and allows you to ...
- 47.7k
40
votes
Accepted
retsubkcolB Spelled Backwards
Solved in 10 moves including "Add a comment" and "Add Comment" buttons at the start and end
I was muddling around in the "inspect element" for way too long trying to ...
- 598
39
votes
Accepted
Find average age without revealing your age
A puts in her age plus a random addition, B, C and D add the same..
Then A removes her addition, then B, C and D do the same.
In equation form where A is the actual age and a is the random addition ...
- 1,942
39
votes
Will a greedy algorithm solve Tatham's Flood?
That problem is NP-hard, so an efficient strategy to calculate the optimal moves would be a major breakthrough in computer science. Of course, there might be a greedy strategy, but not an efficient ...
- 1,065
38
votes
Accepted
Two Sheriffs and Eavesdroppers
Let's say S1 has the list {a,b} and say S2 has {a,c}.
S1: {a,b}, {c,d}, {e,f}, {g,h} - one of these is my list.
S2: {a,c}, {b,d}, {e,g}, {f,h} - one of these is mine.
Now both S1,S2 know their sets ...
- 1,698
38
votes
Accepted
Fairly Sharing a Frosted Cake
We will make all of our cuts vertical, so we can treat this as a square which we need to divide into $10$ pieces with equal slices of the area and the perimeter. This is reasonably easy: Choose $10$ ...
- 7,801
38
votes
Accepted
38
votes
Accepted
lolcatz can haz ur infinit cheeseboard
Unless I'm mistaken, the result is
Reading through the wall of text, the rules seemed a bit too complicated for it to be "just some random game", so figuring out the magic seemed ...
- 72.4k
Only top scored, non community-wiki answers of a minimum length are eligible