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47 votes

Hacking an electronic keypad

My most sincere apologies for this. Really.
Bass's user avatar
  • 77.6k
25 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
  • 366
24 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
  • 77.6k
21 votes
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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
20 votes
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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
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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
  • 77.6k
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
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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
  • 1,584
18 votes
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Transform each square of a chessboard to zero

This is Proof:
Jaap Scherphuis's user avatar
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
  • 18.9k
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
16 votes
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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
  • 136k
16 votes
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Magic: the Gathering – Scry-sort

Assume the N cards are labeled with their desired order, 1 through N. Compare the top two cards and place the smaller of the two on the bottom. Repeat step 1 (N − 1) times. Move the top card to the ...
2012rcampion's user avatar
  • 18.9k
15 votes
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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
  • 21.9k
15 votes
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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
  • 23.6k
15 votes
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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
  • 77.6k
14 votes
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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
  • 7,129
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
  • 2,230
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
13 votes
Accepted

1+3 Towers of Hanoi

From this we get the recursion formula with solution UPDATE As @PM2Ring points out in the comments there is a prettier way of writing the closed formula: The first few values are
Albert.Lang's user avatar
  • 6,057
12 votes

2 Person Same Number Verification

JMP's user avatar
  • 35.6k
12 votes
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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
  • 28.1k
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
11 votes
Accepted

Stacking pancakes for your wife

It can be done in flips. In general case of this puzzle is an open problem called the pancake sorting problem. It is known that with $n$ pancakes the worst case takes somewhere between $\frac{15}{14}...
Jaap Scherphuis's user avatar
11 votes

Two Cannons - A Beginner's Physics Puzzle

They will I did it mathematically Suppose the horizontal distance between both cannons is $d$ and the up angle from right cannon is $\theta$. Then, the left cannon is at a height of $d\tan\...
Alain Remillard's user avatar
11 votes

An $n$-sided polygon with area $n$

Are all $n$ possible? Then is it possible to construct them?
athin's user avatar
  • 34.2k
10 votes

SafeCracker #3 - We've Been Blocked

The doesn't belong, because
19aksh's user avatar
  • 3,933
10 votes
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Cube Scrambling

For a scramble to be any good, at the very least you would want every pair of adjacent pieces to become separated at least once during the scramble. You don't want any blocks to remain unscrambled, ...
Jaap Scherphuis's user avatar

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