Solutions for Act IV Scene 2 - Hazardous

The colours of the numbers suggest that this is a game of minesweeper on a hexagonal grid. As with minesweeper, each value should indicate the number of mines in the neighbouring cells. Judging by the scarcity of blank cells, we must also have mines on cells with numbers.

There is a decision here on whether each number should also include itself, when counting mines. Normally, minesweeper does not have this problem since the mined squares don't have numbers. In our case, however, the natural choice is to only count mines in neighbouring cells, and not itself. This allows for logical deductions which better resembles the ones in normal minesweeper.

A few basic rules based on simple deductions can be formulated to get started:

More advanced techniques are also useful. For example, you can remove existing mines and decrease the surrounding numbers, to reduce complex scenarios to basic ones. The completed grid looks like this:

Now without numbers:

This is a Goomba, an enemy from the Super Mario series. They can be dangerous too, but unlike mines, you would totally step on these!

The answer is: goomba