Krammer said 545 different types of square, but I count 546... (can brains exist on doors?)

There are 21 \"

terrains\"

, 12 of them accept monsters normally; 43 types of monsters; and nine special cases (Baby on Wall, Wraiths on Pits).

9+12*44+9 = 546 (excluding tar, mothers, serpents, savepoints and scrolls)

BUT, only a single blue door can exist, and there are only two configurations of non-adyacent blue doors.

Considering this, the total seems to be:

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×546^4-2*546^2 = 101184468984

Now, to add serpents to the equation...

Serpents can exists on Floor, Trapdoors and Yellow doors (four types of squares only).

A maximum of two serpents can exist on so little room.

Two serpents fill the room, in 8 different configurations. This adds 4^4*8 combinations.

One serpent, four squares length: 8 possibilities. This adds 4^4*8 combinations.

One serpent, three squares length: 8 possibilities. This adds 4^3*8*546 combinations.

One serpent, two squares length: 8 possibilities. This adds 4^2*8*546^2 combinations.

And the total is (excluding tar, mothers, savepoints and scrolls):

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×101184468984 + 38442496 = 101222911480

But the problem is for all legal

**starting** combinations? If so, are monsters allowed over closed doors?