PROBLEM
Invent a method for producing a sequence of zeros and ones not yet listed below. Make sure that your method
would work on a similar square list of any size.
0 1 1 1 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 1 0 1 1 1
0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 1 0 1 1 0
1 0 0 1 0 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 1 0
1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1
0 1 1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0
1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 0
1 1 1 0 1 1 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 0
1 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0
1 1 0 1 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1
1 1 1 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1
1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1
1 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 1 1 1 0 1 0 0 1 1 0
0 1 1 0 1 1 0 1 0 1 0 0 0 0 0 1 1 1 0 1 1 0 1 1 1 1
0 1 1 0 1 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0
1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 0 0 1
1 1 1 1 0 1 0 1 1 1 0 1 0 1 1 1 1 1 1 0 1 0 0 1 0 1
1 1 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 1 1 0 0
1 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 1 0
1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 0 1 0 1 1 0 1 0 1 0 1
0 1 1 1 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 1
0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 1 0 1
0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 0 0 0 0 1 0 1 1
1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 0 1 1 1 1 0 1 0 1
0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 1 0
1 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0
0 0 0 1 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1
Solution
Starting at the upper left corner, go down the diagonal: wherever you see a 0 put a 1 in your
new row, and vice versa. In the present case, here is what you get:
1 0 1 1 0 0 1 0 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0
Your new row cannot be in the list, because it differs from the n-th listed row in the
n-th place (see?).
Conclusion
This works even for an infinite list of infinite rows.
Hence any (denumerable) list of infinite 0,1- sequences is incomplete.