Basically the problem wants you to find the "parent" of given pattern, that is the pattern which will evolute into the given one. If there exists a parent, you print "REACHABLE", otherwise it's "GARDEN OF EDEN". You need backtracking to solve this.
Encoding of the rules is demonstrated in the table in the statement.
Each cell is evaluated, depending on its current state and the state of both its neighbors. Each possible combination (there are just 8 of them) is listed in the table, along with the arbitrarily-chosen new state, which the cell must turn into after the application of the rule. This table is then encoded as 8-bit number by interpreting the numbers in "New state" column as binary digits.
The corresponsing table for identity is:
Left, Cell, Right, New
0 0 0 -> 0
0 0 1 -> 0
0 1 0 -> 1
0 1 1 -> 1
1 0 0 -> 0
1 0 1 -> 0
1 1 0 -> 1
1 1 1 -> 1
Note that the value in "New" column is the same as in the "Cell".
In binary the "New" column is (from bottom to top): 11001100 = 204 (decimal).
See also mathworld's article:
http://mathworld.wolfram.com/Elementary ... maton.html