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59 votes
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Can political debates really work?

I am assuming that So, consider Now,
Gareth McCaughan's user avatar
55 votes
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Is this chromatic puzzle always solvable?

Yes, it's possible. Start with the various 2x2 squares. Ignoring symmetries of rotation and color swapping, there are 1 combination of 1 color, 3 combinations of 2 colors, and 2 combinations of 3 ...
user3294068's user avatar
  • 7,518
50 votes

Transferring 9 pegs on a 9x9 grid

I was having a slow work day, so I fired up Blender and made this: In 13 hops, the block of 9 pegs can be moved two places down and to the right. By repeating the process two more times, the pegs can ...
r3mainer's user avatar
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48 votes
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Pirate democracy at its finest

I have a hunch that the answer is Explanation: Continuing this way, we see that
Glorfindel's user avatar
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47 votes

Hacking an electronic keypad

My most sincere apologies for this. Really.
Bass's user avatar
  • 77.9k
47 votes
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All numbers in a 5x5 Minesweeper grid

Assuming standard Minesweeper rules, here’s one solution (with $ X $ = a mine): EDIT: In response to Euphoric in the comments, I solved this purely by logical deduction with a bit of educated ...
HTM's user avatar
  • 16.3k
47 votes
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Alphabet snake, master of camouflage

How about here: Solve path:
Jafe's user avatar
  • 78.7k
46 votes
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A colorful dodecahedron

Partial Answer: Solution: Other Solutions: Fun Stuff:
DqwertyC's user avatar
  • 8,333
43 votes
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Magnets on a whiteboard

This is a solution
Xoff's user avatar
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34 votes
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Queens attacking exactly one queen

Daniel Mathias's user avatar
34 votes

Two out of a dozen cartons have Easter eggs. Two people try to find one Easter egg carton, each using a different strategy. Who is expected to win?

(context: note that this question is asking for intuitive explanation why it's not equal, so a good answer would have to explain intuitively why the intuition that they will be equal is not the right ...
justhalf's user avatar
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31 votes
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Creating the hardest 6x6 maze

I can make the robot take The robot must take this many steps because
isaacg's user avatar
  • 7,158
30 votes
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Do Langford squares exist?

Langford squares are not possible. Consider the middle two rows of a $2n \times 2n$ Langford square. They, like all rows, must contain $n$'s. Any $n$ must have a partner $n$ in its column that's $n+1$ ...
xnor's user avatar
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28 votes

Winning Strategy for the Magician and his Apprentice

Here is a simple strategy of how they could do it Proof
hexomino's user avatar
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28 votes
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Perfect Golomb Circles

Complete first answer: Yes there exists one for order 5. Consider the combination $1,3,10,2,5$. Partial second answer: A perfect circle of order 98 : $$1, 2, 34, 15, 139, 117, 24, 101, 481, 5, 65,...
Yuzuriha Inori's user avatar
27 votes
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Salesman's claim for mechanical keypad lock - 5 buttons and 545 combinations!

Using only combinations of either single or double button presses: Using 1 press Using 2 presses Using 3 presses Using 4 presses Using 5 presses Total For anyone curious as to my internal ...
Richie Frame's user avatar
27 votes
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France's Public Holidays' Puzzle

First of all, It will probably make a difference So let's concentrate on the other ones We can already stop here; so
Glorfindel's user avatar
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27 votes
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Controlling a robot blindfolded on a 9x9 grid

My first attempt was done by hand. It used 28 commands: but this was not optimal. I have now done a computer search to find optimal solutions. It found 180 solutions of length No shorter solutions ...
Jaap Scherphuis's user avatar
25 votes

Queens attacking exactly one queen

I saw no implications that we aren't going by standard chess rules. Given that we only allow queens to attack the opposing color I propose:
Konstantin Pfennig's user avatar
25 votes
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Selectively neglected collection

These mannequins all have something in common... So what we need to do to assemble the remaining mannequins is too... And as tmpearce points out the comments,
samm82's user avatar
  • 7,242
25 votes
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The shorter the message, the larger the prize

Andrei can send a message that is: How?
fljx's user avatar
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24 votes
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A triangle formed of three letters

We start by proving this is true when the initial row is of length 4. A B C D E F G H I K For any three numbers in the above array P, Q and R, all ...
Mike Earnest's user avatar
  • 32.5k
24 votes

A robot surviving on top of a 3x3 platform

I read the Wired article that was linked in the comments, and applied the ideas mentioned there to this problem, and my computer managed to find a solution that is moves long, and cannot find a ...
Jaap Scherphuis's user avatar
24 votes

How many ways can you find the word DIAMOND in this diamond?

Here is a slightly easier proof than Rand al'Thor's. Let's look at a simpler problem consisting of The number of solutions to this simpler problem is The original problem consists of This easily ...
Jaap Scherphuis's user avatar
23 votes

Twelve balls and a scale

Some of the existing answers to this ancient question are excellent, but there's one famous answer that I think deserves mention here. It comes from an article in Eureka, the annual magazine of the ...
Gareth McCaughan's user avatar
23 votes
Accepted

How many digits can you create with only one seven segment display?

There are Reason:
wythagoras's user avatar
  • 4,133
23 votes

A triangle formed of three letters

Sierpinksi-like triangle mates with pachinko-like machine Following selected funnel-shaped dependencies, a large size-10 triangle recursively breaks down into a size-4-triangle-like arrangement ...
humn's user avatar
  • 21.9k
23 votes

Four buttons on a table

4-button method
hexomino's user avatar
  • 138k
23 votes
Accepted

Princesses covering an 8x8 chess board

Here is the optimal answer with Shown as knights;
Oray's user avatar
  • 30.4k
23 votes

Minimize 1×3 tiles on a 5×5 table to block any more 1×3 tiles

UPDATE 2: To put OP out of their misery find now at the very bottom of this post an answer to what they probably mean. UPDATE: OP has changed the rules, so this is no longer valid, but see bottom of ...
loopy walt's user avatar
  • 21.3k

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