---
id: 5900f43e1000cf542c50ff4f
title: 'Problem 209: Circular Logic'
challengeType: 5
forumTopicId: 301850
dashedName: 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)?

# --hints--

`euler209()` should return 15964587728784.

```js
assert.strictEqual(euler209(), 15964587728784);
```

# --seed--

## --seed-contents--

```js
function euler209() {

  return true;
}

euler209();
```

# --solutions--

```js
// solution required
```