79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
89 lines
2.3 KiB
Markdown
89 lines
2.3 KiB
Markdown
---
|
|
title: Babbage problem
|
|
id: 594db4d0dedb4c06a2a4cefd
|
|
challengeType: 5
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
<p><a href="https://en.wikipedia.org/wiki/Charles_Babbage" title="wp: Charles_Babbage">Charles Babbage</a>, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:</p>
|
|
<blockquote>What is the smallest positive integer whose square ends in the digits 269,696?</blockquote>
|
|
<p> - Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, <i>Electronic Computers</i>, second edition, 1970, p. 125.</p>
|
|
<p>He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.</p>
|
|
<p>The task is to find out if Babbage had the right answer.</p>
|
|
<p>Implement a function to return the lowest integer that satisfies the Babbage problem. If Babbage was right, return Babbage's number.</p>
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>babbage</code> is a function.
|
|
testString: assert(typeof babbage === 'function', '<code>babbage</code> is a function.');
|
|
- text: <code>babbage(99736, 269696)</code> should not return 99736 (there is a smaller answer).
|
|
testString: assert.equal(babbage(babbageAns, endDigits), answer, '<code>babbage(99736, 269696)</code> should not return 99736 (there is a smaller answer).');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function babbage (babbageNum, endDigits) {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
### After Test
|
|
<div id='js-teardown'>
|
|
|
|
```js
|
|
const babbageAns = 99736;
|
|
const endDigits = 269696;
|
|
const answer = 25264;
|
|
```
|
|
|
|
</div>
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
|
|
```js
|
|
function babbage (babbageAns, endDigits) {
|
|
const babbageNum = Math.pow(babbageAns, 2);
|
|
const babbageStartDigits = parseInt(babbageNum.toString().replace('269696', ''));
|
|
let answer = 99736;
|
|
|
|
// count down from this answer and save any sqrt int result. return lowest one
|
|
for (let i = babbageStartDigits; i >= 0; i--) {
|
|
const num = parseInt(i.toString().concat('269696'));
|
|
const result = Math.sqrt(num);
|
|
if (result === Math.floor(Math.sqrt(num))) {
|
|
answer = result;
|
|
}
|
|
}
|
|
|
|
return answer;
|
|
}
|
|
|
|
```
|
|
|
|
</section>
|