2.3 KiB
2.3 KiB
| title | id | challengeType |
|---|---|---|
| Babbage problem | 594db4d0dedb4c06a2a4cefd | 5 |
Description
Charles Babbage, looking ahead to the sorts of problems his Analytical Engine would be able to solve, gave this example:
What is the smallest positive integer whose square ends in the digits 269,696?
- Babbage, letter to Lord Bowden, 1837; see Hollingdale and Tootill, Electronic Computers, second edition, 1970, p. 125.
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.
Implement a function to return the lowest integer that satisfies the Babbage problem. If Babbage was right, return Babbage's number.
Instructions
Tests
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).');
Challenge Seed
function babbage (babbageNum, endDigits) {
// Good luck!
return true;
}
After Test
const babbageAns = 99736;
const endDigits = 269696;
const answer = 25264;
Solution
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;
}