48 votes

Hacking an electronic keypad

My most sincere apologies for this. Really.
Bass's user avatar
  • 72.4k
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 ...
xnor's user avatar
  • 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 ...
Deusovi's user avatar
  • 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 ...
Julian Rosen's user avatar
  • 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 ...
GOTO 0's user avatar
  • 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 ...
Bass's user avatar
  • 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 ...
klm123's user avatar
  • 16k
21 votes
Accepted

Checkerboard Infection

This is a pretty common puzzle. Warm up Answer: Advanced Answer Explanation:
qwertylpc's user avatar
  • 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 ...
noedne's user avatar
  • 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 ...
IAmInPLS's user avatar
  • 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 ...
mmk's user avatar
  • 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 ...
Bass's user avatar
  • 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 ...
npkllr's user avatar
  • 1,554
18 votes
Accepted

Transform each square of a chessboard to zero

This is Proof:
Jaap Scherphuis's user avatar
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:
Anon's user avatar
  • 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:
2012rcampion's user avatar
  • 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 ...
noedne's user avatar
  • 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 ...
Lawrence's user avatar
  • 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 ...
Rand al'Thor's user avatar
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:
Zerris's user avatar
  • 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 ...
hexomino's user avatar
  • 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 ...
humn's user avatar
  • 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, ...
Dr Xorile's user avatar
  • 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 ...
Bass's user avatar
  • 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, ...
qwertylpc's user avatar
  • 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. ...
Florian F's user avatar
  • 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:
isaacg's user avatar
  • 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 ...
Quuxplusone's user avatar
  • 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.
Jaap Scherphuis's user avatar
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 ...
Puzzle Prime's user avatar
  • 6,934

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