48 votes

Hacking an electronic keypad

My most sincere apologies for this. Really.
Bass's user avatar
  • 75.9k
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
  • 145k
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
  • 13.5k
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
  • 75.9k
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
  • 16.1k
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
  • 15.4k
21 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
  • 326
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
  • 11.5k
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
  • 75.9k
19 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
  • 15.4k
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
  • 1,564
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
  • 18.6k
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
  • 4,671
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
  • 133k
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
  • 22.8k
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
  • 75.9k
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
  • 26.8k
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
  • 5,431
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
  • 1,770
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

Rank the Fencers

There are $5!=120$ possible orderings of the fencers, so we need $\log_2(120)\approx 6.9069$ bits of information. Each duel provides at most $1$ bit of information, so at least $7$ duels will be ...
Julian Rosen's user avatar
  • 14.2k
12 votes
Accepted

Half-reverse operation on binary strings

Consider the set of binary strings that are lexicographically earlier than their reverses. For example, 011, 1011, and ...
f'''s user avatar
  • 33.6k
12 votes

2 Person Same Number Verification

JMP's user avatar
  • 35.6k
12 votes
Accepted

GameDev: stuck with first puzzle design, would love resources to study from or algorithm suggestions!

This is related to the mathematical field of graph theory, and your puzzle is essentially a finite-state machine. Each platform has 8 possible states, so the entire system has $8^3=512$ states ('...
Glorfindel's user avatar
  • 27.9k
12 votes

The dessert problem (blind ballot remaining blind if non-unanimous)

I know nothing about the "black balling" method mentioned in the problem, but hearing the term got me thinking about an easy solution: The only issue I see with this system is: Edited to ...
Amorydai's user avatar
  • 2,963
11 votes
Accepted

Is it possible to scramble a Rubik's cube so that each face has no more than 2 squares of the same color?

Yes it is possible! Do you know how to get it into a checkered state? Looking at any face you then do as follows.... Keep the same face towards you the entire time. Turn left side clock-wise Turn ...
Saloaty's user avatar
  • 126

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