There is no need to test all cases. The ideal case is a swiss cheese in which no guest share a wall. Just start filling rooms from there if needed (the only problems is that room filling must follow an order, which makes the code quite large (but repetitive and boring), and there are two base cases for the swiss cheese structure). Maybe it's possible to create a function and decrease code size, but unless you see it at the moment that you are coding it, it would mean loosing too much time during competition when a Ctrl+C, Ctrl+V would be faster (and better than testing all cases).
Currently, my solutions and this one are the only that don't use brute force, but this one is the smallest. Congrats. :) (I was able to create a smaller solution after looking at your code.)
How to find the position of an element in a vector without using the find function
Count from 0 to N^M in base N.
Determine if input is a perfect number
Subtract two positive numbers
convert matrix to single column
USC Fall 2012 ACM Question A : Read Input File
QWERTY Shift Encoder
Kurchan Square - Evaluation Function
Kurchan 3x3 - Optimal Score
Maximize Non-Co-Planar Points in an N-Cube
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