# Tag Info

Accepted

### Can political debates really work?

I am assuming that So, consider Now,
• 120k
Accepted

### 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 ...
• 7,518

### 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 ...
• 9,791
Accepted

### Pirate democracy at its finest

I have a hunch that the answer is Explanation: Continuing this way, we see that
• 28.1k

My most sincere apologies for this. Really.
• 77.9k
Accepted

### 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 ...
• 16.3k
Accepted

• 78.7k
Accepted

### A colorful dodecahedron

Partial Answer: Solution: Other Solutions: Fun Stuff:
• 8,333
Accepted

### Magnets on a whiteboard

This is a solution
• 814
Accepted

• 15.4k

### 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 ...
• 6,042
Accepted

### Creating the hardest 6x6 maze

I can make the robot take The robot must take this many steps because
• 7,158
Accepted

### 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 $n+1$ ...
• 27.4k

### Winning Strategy for the Magician and his Apprentice

Here is a simple strategy of how they could do it Proof
• 138k
Accepted

### 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,...
• 1,173
Accepted

### 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 ...
• 394
Accepted

### 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
• 28.1k
Accepted

### 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 ...
• 53.8k

### 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:
Accepted

### 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,
• 7,242
Accepted

### The shorter the message, the larger the prize

Andrei can send a message that is: How?
• 16.6k
Accepted

### 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 ...
• 32.5k

### 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 ...
• 53.8k

### 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 ...
• 53.8k

### 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 ...
• 120k
Accepted

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

There are Reason:
• 4,133

### 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 ...
• 21.9k

4-button method
• 138k
Accepted

### Princesses covering an 8x8 chess board

Here is the optimal answer with Shown as knights;
• 30.4k