# Problem 209: Circular Logic

![graphic](img209.gif)

A k-input binary truth table is a map from k input bits (binary digits,
0 \[false\] or 1 \[true\]) to 1 output bit. For example, the 2-input
binary truth tables for the logical AND and XOR functions are: x y x AND
y000010100111x y x XOR y000011101110How many 6-input binary truth
tables, τ, satisfy the formula τ(a, b, c, d, e, f) AND τ(b, c, d, e, f,
a XOR (b AND c)) = 0 for all 6-bit inputs (a, b, c, d, e, f)?