Problem 209
Circular Logic

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 y
0 0 0
0 1 0
1 0 0
1 1 1
x y x XOR y
0 0 0
0 1 1
1 0 1
1 1 0

How 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)?

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http://projecteuler.net/problem=209