---
id: 5900f4281000cf542c50ff39
title: 'Problem 186: Connectedness of a network'
challengeType: 5
forumTopicId: 301822
dashedName: problem-186-connectedness-of-a-network
---

# --description--

Here are the records from a busy telephone system with one million users:

RecNrCallerCalled120000710005326001835004393600863701497......... The telephone number of the caller and the called number in record n are Caller(n) = S2n-1 and Called(n) = S2n where S1,2,3,... come from the "Lagged Fibonacci Generator":

For 1 ≤ k ≤ 55, Sk = \[100003 - 200003k + 300007k3] (modulo 1000000) For 56 ≤ k, Sk = \[Sk-24 + Sk-55] (modulo 1000000)

If Caller(n) = Called(n) then the user is assumed to have misdialled and the call fails; otherwise the call is successful.

From the start of the records, we say that any pair of users X and Y are friends if X calls Y or vice-versa. Similarly, X is a friend of a friend of Z if X is a friend of Y and Y is a friend of Z; and so on for longer chains.

The Prime Minister's phone number is 524287. After how many successful calls, not counting misdials, will 99% of the users (including the PM) be a friend, or a friend of a friend etc., of the Prime Minister?

# --hints--

`euler186()` should return 2325629.

```js
assert.strictEqual(euler186(), 2325629);
```

# --seed--

## --seed-contents--

```js
function euler186() {

  return true;
}

euler186();
```

# --solutions--

```js
// solution required
```