55 lines
997 B
Markdown
55 lines
997 B
Markdown
|
---
|
||
|
|
id: 5900f4021000cf542c50ff14
|
||
|
|
title: 'Problem 148: Exploring Pascal''s triangle'
|
||
|
|
challengeType: 5
|
||
|
|
forumTopicId: 301777
|
||
|
|
dashedName: problem-148-exploring-pascals-triangle
|
||
|
|
---
|
||
|
|
|
||
|
|
# --description--
|
||
|
|
|
||
|
|
We can easily verify that none of the entries in the first seven rows of Pascal's triangle are divisible by 7:
|
||
|
|
|
||
|
|
<pre>
|
||
|
|
1
|
||
|
|
1 1
|
||
|
|
1 2 1
|
||
|
|
1 3 3 1
|
||
|
|
1 4 6 4 1
|
||
|
|
1 5 10 10 5 1
|
||
|
|
1 6 15 20 15 6 1
|
||
|
|
</pre>
|
||
|
|
|
||
|
|
However, if we check the first one hundred rows, we will find that only 2361 of the 5050 entries are not divisible by 7.
|
||
|
|
|
||
|
|
# --instructions--
|
||
|
|
|
||
|
|
Find the number of entries which are not divisible by 7 in the first one billion (10<sup>9</sup>) rows of Pascal's triangle.
|
||
|
|
|
||
|
|
# --hints--
|
||
|
|
|
||
|
|
`euler148()` should return 2129970655314432.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.strictEqual(euler148(), 2129970655314432);
|
||
|
|
```
|
||
|
|
|
||
|
|
# --seed--
|
||
|
|
|
||
|
|
## --seed-contents--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function euler148() {
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
euler148();
|
||
|
|
```
|
||
|
|
|
||
|
|
# --solutions--
|
||
|
|
|
||
|
|
```js
|
||
|
|
// solution required
|
||
|
|
```
|