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### Solutions for Act II Scene 3 - B Hive

We seem to have been presented with a word search puzzle, albeit in a hexagonal grid. Since there isn't much else to do at this point, we may as well find all the (more than two-letter) words hidden in the grid:

The next step is the trickiest leap to make: Each of these words can precede or follow the name of a common bug to make a familiar phrase. This step is hinted at by the presentation and title, with the likeliest culprit probably SPELLING, which can precede BEE. The phrases that can be deduced are:

spelling bee
busy bee
ant-hill
ant farm
antacid
spider sense
young grasshopper
beetlejuice

Next, one needs to realise this is actually a disguised game of Hive, a game played with hexagonal pieces featuring each of the creatures discovered in the first step. This can be found out by Googling some of the bugs' names once found, and is also heavily hinted by the title to help out those who have never heard of the game.

In order to place the pieces, we must use the phrases we've discovered. It turns out the correct placement involves placing the pieces so that they complete their respective phrases - for example, to complete the phrase "busy bee" we would need the Q cell to represent a bee tile. This trick is again hinted at by the title B-Hive, which is implying letters might stand for bug names in this puzzle. Placing all the pieces gives us the following configuration:

That the beetle lies on the same space as an ant is not a problem since in Hive, the beetle's ability is to climb on top of other pieces. That one of the bees is found in the only dark cell is also promising, since this would imply it is the only black piece in the game (and the bee is the only required piece in play for a proper game of Hive).

Now all that remains is to play the game through. We assume as per usual that White plays first, and since it has far more room for variance, we can assume we are playing as White. Indeed there is also a hidden message down the right of the whole hive which reads "YOU CAN'T ADD WHITE(S)", which also informs us of a house rule in this puzzle: No more new white pieces can be added to the board. This is useful since it severely limits our move options. (Also, note this message suggests some sort of game is in process, being another useful hint that this puzzle is based on Hive).

It turns out that the optimal way for White to win (i.e. the way for White to legally surround the black bee in the least number of moves) is in exactly eight moves, and moreover these moves are unique up to ordering. The first move must be moving the only free ant to the opposite side of the black bee, to force Black into not being able to add any new pieces and thus unable to move at all. The optimal strategy looks like this:

 Ant N -> M (to prevent Black from being able to add any of their own pieces to the game) Beetle E -> A (to free up the ant it's on top of) Grasshopper S -> R (to make room for the white Bee's fastest reconnection to the hive) Bee D -> S (to ensure its connection to the hive) Ant E -> H (to begin surrounding the black Bee, since this Ant is now free to move) Grasshopper R -> F (to surround the black Bee) Spider Y -> L (since it can finally move to a Bee-surrounding position) Beetle A -> Y (to finish capturing the black Bee)

Note this last move is the only one that can actually happen at any time in the sequence after the fourth move, however it's assumed it's most naturally moved last since the other (optimally) forced moves happen in a logically uninterrupted order. Finally we can note that the letters landed on in this order give the name MARSH FLY, the common name for another kind of bug (which is itself a fly, while one of Hive's expansion pieces is the Mosquito).

Design Notes:
It's unfortunately very difficult to create a Hive game in which the optimal solution's order is both unique and completely ordered. Having only one move whose position in the sequence is uncertain was the best game I could create that wasn't trivially solved.

The answer phrase was deliberately chosen to be a less common bug's name so that it wouldn't turn up in anagram engines, since the observant solver can quickly predict the answer extraction method and try guessing the answer based on the letters surrounding the black cell.