48
votes
33
votes
Accepted
Maze Solving Robot
Sure you can. There's finitely many possible mazes, so solve each one in sequence. To solve a maze, imagine you're in that maze. Figure out where you are in the maze by simulating starting on the ...
- 24.6k
30
votes
Accepted
Desegregate the Knights
Give these names to all the squares:
163
4 8
725
Each number can only be accessed by way of the numbers before and after it (where 8 wraps around to 1). That ...
- 144k
28
votes
Accepted
Radioactive Rods
In the worst-case scenario, it requires
to locate the radioactive rods. Several answers already describe strategies for locating the radioactive rods. I will give another.
Testing strategy: Start ...
- 14.1k
27
votes
Switch The Knights
I found a solution that uses 16 moves.
After exhaustively checking that there is no solution in 14 moves, I conclude that 16 moves is optimal, because after any odd number of moves the number of ...
- 13.4k
23
votes
Accepted
Two Cannons - A Beginner's Physics Puzzle
Alain Remillard has given the mathematician's answer. Here's the physicist's one:
Step 1:
Obviously, in such a universe, regardless of their speed, the cannonballs will travel in a straight line and ...
- 72.4k
22
votes
Accepted
Switch The Knights
You need at least 16 Moves.
Let's make the task visually more simple. The initial board is:
a4 b4 c4
a3 b3 c3
a2 b2 c2
a1 b1 c1
We cut it into 12 cells ...
- 16k
21
votes
Accepted
Checkerboard Infection
This is a pretty common puzzle.
Warm up Answer:
Advanced Answer Explanation:
- 1,519
21
votes
Accepted
Wolves and sheep
Perform
tests of nine sheep on all but one sheep according to the illustrated patterns:
The two important properties exhibited are
The claim is that given a set of test results there is at most one ...
- 15.3k
20
votes
Accepted
Mystery operation
Ok, I think I got something. The answer should be :
The ancient civilization
The operation *|* is performed :
Now, the real problem. In order to obtain the ...
- 11.4k
20
votes
Accepted
What's the optimal strategy for Wordle?
Assumptions:
Optimal firstly means never losing (rather than some definition of a good average depth).
The 12972 words in the Wordle source code are the only valid guesses.
The target word is ...
- 316
19
votes
Accepted
Hacking an electronic keypad
As atonement for my insolent lateral-thinking answer, I offer an optimality proof.
If you keep repeating the correct code, the are six possible different orders:
1 abcdabcdabcd
2 abdcabdcabdc
3 ...
- 72.4k
18
votes
Accepted
Three knights searching for a princess in a castle
The knights need a maximum of:
I made a quick drawing to show my strategy. The yellow squares are the rooms the knights look into that night, the black squares are rooms in which the princess ...
- 1,554
18
votes
Accepted
17
votes
Can you recreate this fractal I randomly made?
There are only 16 different possible state combinations of the four ancestor cells, and you can find them all in the image, so there is a unique answer.
The rule is as follows:
- 2,684
17
votes
Accepted
Can you recreate this fractal I randomly made?
The pattern is self-similar, and can be formed by repeatedly scaling and rotating copies of itself:
An alternate dissection that fits in a diamond:
- 17.2k
17
votes
Accepted
Exterminating blobs on a grid
Given an arrangement of blobs, how can you determine whether it is possible to exterminate them all?
What strategy can you use to succeed when possible?
Warning: what follows is a constructive but ...
- 15.3k
16
votes
Confused Soldiers
A series of variants of this puzzle came up in one of the trade magazines - possibly Communications of the ACM.
When two soldiers face each other, they are required to turn around. Assuming the ...
- 7,849
16
votes
Confused Soldiers
Treat each soldier as a binary digit, $1$ if facing east and $0$ if facing west, and order them from west to east (i.e. left to right). We start off with a random $n$-digit binary number, and the ...
- 115k
16
votes
Switch The Knights
Edit: Now that @GOTO 0 got it in 16, I can at least prove that his solution is optimal.
Proof:
My best was:
- 4,661
16
votes
Accepted
Worst way to solve Rubik's in one algorithm
It seems like you are trying to find
One such example that satisfies this is
In particular,
As mentioned by armb in the comments, there is a good answer here discussing the maximum orders for an $n ...
- 131k
15
votes
Accepted
Consecutive Towers of Hanoi
Here is a revised solution, for...
...which (again) seems like the maximum to me.
has been
verified by Molhan
as being maximal.
Trivial steps have been condensed.
These ...
- 21.8k
15
votes
Accepted
2 Person Same Number Verification
Any commutative hash function will do.
Using RSA makes this relatively easy, I think.
So Alice and Beth both establish their secret primes,
and, in a twist, keep everything secret.
$ % Make EA, EB, ...
- 22.4k
15
votes
Accepted
Programmatically solving a math puzzle with four unknowns and four equations
First of all, let's see why your brute-forcing fails. (This is the puzzle part, the rest is plain old math.)
No matter which you chose, the number at the bottom right would have to be both odd and ...
- 72.4k
14
votes
Checkerboard Infection: The Aftermath
Not exactly answering this question, but given 9 infections still on an 8x8 board, it is actually possible to delay the inevitable until 40 days. Pretty counter-intuitive huh?
Locations are A1, A5, ...
- 1,519
14
votes
23 Clones and Two Lightbulbs
The standard solution is that all clones signal their first passage using some state of the bulbs to an elected clone, the "counter", who counts how many there are.
You need to address 3 things.
1. ...
- 25.1k
14
votes
Accepted
Blindfold Bingo
I have a solution with a success rate of 93.5%, according to my simulations.
The reason this solution works so well is
Here's my code that I used to verify my solution:
- 4,238
13
votes
Wolves and sheep
Thinking out loud, not a solution yet, but spoilery enough that I didn't want to put it in a comment:
However,
Still-not-an-answer UPDATE:
However,
I also notice that the situation is not ...
- 1,691
13
votes
Accepted
Find Local Maximum in an Integer Sequence
It is possible to solve up to $n=20$ cells using only $m=6$ moves.
In particular, it is not possible to answer the bonus question as stated.
- 47.7k
12
votes
Accepted
Checkerboard Infection: The Aftermath
EDITED - thanks to @Meelo for pointing out my mistake.
We can do it in
We place the C.Coli's at a4, a8, b2, c1, e2, g1, h3, h6.
Now we prove that this is optimal. Every day there are either 1 new ...
- 6,934
Only top scored, non community-wiki answers of a minimum length are eligible