79 lines
1.9 KiB
Markdown
79 lines
1.9 KiB
Markdown
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---
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id: 594db4d0dedb4c06a2a4cefd
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title: Babbage problem
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challengeType: 5
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forumTopicId: 302229
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dashedName: babbage-problem
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---
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# --description--
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[Charles Babbage](https://en.wikipedia.org/wiki/Charles_Babbage "wp: Charles_Babbage"), looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
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<blockquote>
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What is the smallest positive integer whose square ends in the digits 269,696?
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<footer style='margin-left: 2em;'>Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, <i>Electronic Computers</i>, second edition, 1970, p. 125.</footer>
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</blockquote>
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He thought the answer might be 99,736, whose square is 9,947,269,696; but he couldn't be certain.
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The task is to find out if Babbage had the right answer.
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# --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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# --hints--
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`babbage` should be a function.
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```js
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assert(typeof babbage === 'function');
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```
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`babbage(99736, 269696)` should not return 99736 (there is a smaller answer).
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```js
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assert.equal(babbage(babbageAns, endDigits), answer);
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```
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# --seed--
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## --after-user-code--
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```js
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const babbageAns = 99736;
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const endDigits = 269696;
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const answer = 25264;
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```
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## --seed-contents--
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```js
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function babbage(babbageNum, endDigits) {
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return true;
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}
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```
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# --solutions--
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```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;
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// count down from this answer and save any sqrt int result. return lowest one
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for (let i = babbageStartDigits; i >= 0; i--) {
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const num = parseInt(i.toString().concat('269696'));
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const result = Math.sqrt(num);
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if (result === Math.floor(Math.sqrt(num))) {
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answer = result;
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}
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}
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return answer;
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}
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```
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