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
for all 6-bit inputs (a, b, c, d, e, f)?
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK