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---
title: Babbage problem
id: 594db4d0dedb4c06a2a4cefd
challengeType: 5
---
## Description
< section id = 'description' >
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< a href = "https://en.wikipedia.org/wiki/Charles_Babbage" title = "wp: Charles_Babbage" target = '_blank' > Charles Babbage< / a > , looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
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< blockquote >
What is the smallest positive integer whose square ends in the digits 269,696?
< footer > Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, < i > Electronic Computers< / i > , second edition, 1970, p. 125.< / footer >
< / blockquote >
He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
The task is to find out if Babbage had the right answer.
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< / section >
## Instructions
< section id = 'instructions' >
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Implement a function to return the lowest integer that satisfies the Babbage problem. If Babbage was right, return Babbage's number.
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< / section >
## Tests
< section id = 'tests' >
```yml
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tests:
- text: < code > babbage</ code > is a function.
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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).');
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```
< / section >
## Challenge Seed
< section id = 'challengeSeed' >
< div id = 'js-seed' >
```js
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function babbage(babbageNum, endDigits) {
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// Good luck!
return true;
}
```
< / div >
### After Test
< div id = 'js-teardown' >
```js
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const babbageAns = 99736;
const endDigits = 269696;
const answer = 25264;
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```
< / div >
< / section >
## Solution
< section id = 'solution' >
```js
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function babbage(babbageAns, endDigits) {
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const babbageNum = Math.pow(babbageAns, 2);
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const babbageStartDigits = parseInt(babbageNum.toString().replace('269696', ''));
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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 >