# Tag Info

Accepted

• 464

### 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
Accepted

### Wizard of subsets

Unless I'm missing something
• 2,440

### Wizard of subsets

Move those marked l to the left, then the rs right and then the us up.
• 16.3k

### Wizard of subsets

Very similar to @loopy-walt solution, but still OC :)
• 651
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
• 2,440

### 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

### 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

### Mixing liquids in bottles

Note a couple of lemmata. Also Now, Now From this point onwards Informally I suspect
• 2,440
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 ...
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

### 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 ...
• 28.9k

### 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

### 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

(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
1 vote

### Attacking Hyenas

We can slightly rephrase this question as "For a given number of attacked hyenas, what is the maximum number of unattacked hyenas we can have?" Particularly, since hyenas can be divided into ...
• 6,932
1 vote

### Attacking Hyenas

The following presents the maximum number of unattacked hyenas alongside their corresponding ratio: and here is the representation of this; and here is a better representation with the right ...
• 29.6k

Only top scored, non community-wiki answers of a minimum length are eligible