---
id: 5900f43e1000cf542c50ff4f
challengeType: 5
title: 'Problem 209: Circular Logic'
---
## Description
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)?
## Instructions
## Tests
```yml
tests:
- text: euler209() should return 15964587728784.
testString: assert.strictEqual(euler209(), 15964587728784, 'euler209() should return 15964587728784.');
```
## Challenge Seed
```js
function euler209() {
// Good luck!
return true;
}
euler209();
```