# Tag Info

### Wizard of subsets

Very similar to @loopy-walt solution, but still OC :)
• 581

### Wizard of subsets

Move those marked l to the left, then the rs right and then the us up.
• 16.2k

### Wizard of subsets

Unless I'm missing something
• 2,355
Accepted

### What's the most distant chess position?

This question was asked on Chess Stack Exchange a couple of years ago: Which chess position requires the most moves to reach? Just like @loopywalt here in the comments, I remembered Tim Krabbé's diary ...
• 27.3k

### What's the most distant chess position?

I will open the bidding at I won’t offer a series of moves, but describe the position as To see that this would take at least as many moves as claimed, note that In fact
• 2,355

### Fair d5 with as few faces as possible

I think 6 sides would suffice. Make it fairly tall compared to the pentagon at the base, and "roll" it by spinning it like a top. If, by some miracle of fate, it manages to balance on the ...
• 131

### Fair d5 with as few faces as possible

If the die is not required to be convex, and faces are not required to be simple polygons, I think one could fabricate a nine-faced die by taking a five-sided pyramid and attaching a very long and ...
• 2,167
Accepted

### Fair d5 with as few faces as possible

By "symmetric", I mean that there should exist symmetries of the polyhedron mapping each of the five stable faces to each other. Sets of independent symmetry elements The symmetry of a ...

### Fair d5 with as few faces as possible

Surely will suffice for all n > 2. Consider a symmetrical cone with an n-sided regular polygon as its base. If we take a "stubby" one (of a shortish height) and a "pointy" one (...
• 71.5k

### How much money can we make?

Well I am a bit late to the party, but I did manage to find another solution that gives the same amount as the accepted answer: giving the final amounts: For the 7 person version of the problem my ...
• 28.8k

### Boxeslayers to the rescue

(This is not an answer to the 183 problem asked here) High efficiency packing (arbitrary close to 100%) for far larger numbers of boxes
• 6,847

### Mixing liquids in bottles

Note a couple of lemmata. Also Now, Now From this point onwards Informally I suspect
• 2,355
Accepted

### Mixing liquids in bottles

I have no proof that this is the best possible. After the following steps Then you end up with the following in bottle 1: For comparison, I'll divide by $4$ litres to get the composition fractions.
• 47.3k

### Mixing liquids in bottles

Nearest Attempt so far If we do the following steps Then you end up with the following in bottle 1 Of course, if we remove the last two steps from the procedure then bottle 1 contains the following
• 130k

### Boxeslayers to the rescue

Here is one way to do it, showing the pattern along with its mirror image. The rectangular area is 83 x 24 units, or 1992 square units. And the two combined, to show that this is a safe stacking ...
• 11.3k

### Most polyominoes in an 8x8 grid

Controversial answer: Credits to @RobPratt for image.
Accepted

• 464

### Most polyominoes in an 8x8 grid

If polyominoes of the same color can share an edge and polyominoes of different colors are considered distinct, the maximum is Under the intended interpretation (polyominoes of the same color cannot ...
• 10.2k

### A Queen and her Pawns

Solved the 19 pawn puzzle flipping the ending pawn to the queen and working backwards. Original position by @Oray Starts at e2: a6,a4,d7,c8,c3,f6,g7,f7,b7,a7,h7,h8,h6,d6,d8,g5,f5,b1,h1
• 31