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curriculum/challenges/italian/10-coding-interview-prep/rosetta-code/babbage-problem.md

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+---
+id: 594db4d0dedb4c06a2a4cefd
+title: Babbage problem
+challengeType: 5
+forumTopicId: 302229
+dashedName: babbage-problem
+---
+
+# --description--
+
+[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:
+
+<blockquote>
+  What is the smallest positive integer whose square ends in the digits 269,696?
+  <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>
+</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.
+
+# --instructions--
+
+Implement a function to return the lowest integer that satisfies the Babbage problem. If Babbage was right, return Babbage's number.
+
+# --hints--
+
+`babbage` should be a function.
+
+```js
+assert(typeof babbage === 'function');
+```
+
+`babbage(99736, 269696)` should not return 99736 (there is a smaller answer).
+
+```js
+assert.equal(babbage(babbageAns, endDigits), answer);
+```
+
+# --seed--
+
+## --after-user-code--
+
+```js
+const babbageAns = 99736;
+const endDigits = 269696;
+const answer = 25264;
+```
+
+## --seed-contents--
+
+```js
+function babbage(babbageNum, endDigits) {
+
+  return true;
+}
+```
+
+# --solutions--
+
+```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;
+}
+```