yaworsw/euler-manager

---
:id: 209
:name: Circular Logic
:url: https://projecteuler.net/problem=209
:content: "A <var>k</var>-input _binary truth table_ is a map from <var>k</var> 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:\n\n| <var>x</var>
  | <var>y</var> | <var>x</var> AND <var>y</var> |\n| 0 | 0 | 0 |\n| 0 | 1 | 0 |\n|
  1 | 0 | 0 |\n| 1 | 1 | 1 |\n\n| <var>x</var> | <var>y</var> | <var>x</var> XOR <var>y</var>
  |\n| 0 | 0 | 0 |\n| 0 | 1 | 1 |\n| 1 | 0 | 1 |\n| 1 | 1 | 0 |\n\n  \n\nHow many
  6-input binary truth tables, τ, satisfy the formula\n\nτ(<var>a</var>, <var>b</var>,
  <var>c</var>, <var>d</var>, <var>e</var>, <var>f</var>) AND τ(<var>b</var>, <var>c</var>,
  <var>d</var>, <var>e</var>, <var>f</var>, <var>a</var> XOR (<var>b</var> AND <var>c</var>))
  = 0\n  \n\nfor all 6-bit inputs (<var>a</var>, <var>b</var>, <var>c</var>, <var>d</var>,
  <var>e</var>, <var>f</var>)?\n\n"