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 | x | y | x XOR y | |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | |
| 0 | 1 | 0 | 0 | 1 | 1 | |
| 1 | 0 | 0 | 1 | 0 | 1 | |
| 1 | 1 | 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)?
圆环之理
k元真值表是从k比特位（即二进制位的简称，其中0代表假，1代表真）输入到1比特位输出的映射。例如，逻辑运算符AND（和）和XOR（异或）的2元真值表如下所示：
| x | y | x AND y | x | y | x XOR y | |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | |
| 0 | 1 | 0 | 0 | 1 | 1 | |
| 1 | 0 | 0 | 1 | 0 | 1 | |
| 1 | 1 | 1 | 1 | 1 | 0 |
有多少个6元真值表τ，对于所有的6比特位输入(a, b, c, d, e, f)始终满足下述等式？