ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
114 lines
2.9 KiB
Markdown
114 lines
2.9 KiB
Markdown
---
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id: 5900f3a31000cf542c50feb6
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title: 'Problem 55: Lychrel numbers'
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challengeType: 5
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forumTopicId: 302166
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dashedName: problem-55-lychrel-numbers
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---
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# --description--
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If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
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Not all numbers produce palindromes so quickly. For example,
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<div style="margin-left: 4em;">
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349 + 943 = 1292,<br>
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1292 + 2921 = 4213<br>
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4213 + 3124 = 7337<br>
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</div>
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That is, 349 took three iterations to arrive at a palindrome.
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Although no one has proved it yet, it is thought that some numbers, like 196, never produce a palindrome. A number that never forms a palindrome through the reverse and add process is called a Lychrel number. Due to the theoretical nature of these numbers, and for the purpose of this problem, we shall assume that a number is Lychrel until proven otherwise. In addition you are given that for every number below ten-thousand, it will either (i) become a palindrome in less than fifty iterations, or, (ii) no one, with all the computing power that exists, has managed so far to map it to a palindrome. In fact, 10677 is the first number to be shown to require over fifty iterations before producing a palindrome: 4668731596684224866951378664 (53 iterations, 28-digits).
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Surprisingly, there are palindromic numbers that are themselves Lychrel numbers; the first example is 4994.
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How many Lychrel numbers are there below `num`?
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**Note:** Wording was modified slightly on 24 April 2007 to emphasize the theoretical nature of Lychrel numbers.
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# --hints--
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`countLychrelNumbers(1000)` should return a number.
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```js
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assert(typeof countLychrelNumbers(1000) === 'number');
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```
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`countLychrelNumbers(1000)` should return 13.
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```js
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assert.strictEqual(countLychrelNumbers(1000), 13);
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```
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`countLychrelNumbers(3243)` should return 39.
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```js
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assert.strictEqual(countLychrelNumbers(3243), 39);
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```
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`countLychrelNumbers(5000)` should return 76.
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```js
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assert.strictEqual(countLychrelNumbers(5000), 76);
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```
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`countLychrelNumbers(7654)` should return 140.
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```js
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assert.strictEqual(countLychrelNumbers(7654), 140);
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```
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`countLychrelNumbers(10000)` should return 249.
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```js
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assert.strictEqual(countLychrelNumbers(10000), 249);
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```
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# --seed--
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## --seed-contents--
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```js
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function countLychrelNumbers(num) {
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return true;
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}
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countLychrelNumbers(10000);
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```
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# --solutions--
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```js
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const countLychrelNumbers = (size) => {
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const numReverse = (num) => {
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return Number(num.toString().split('').reverse().join(''));
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};
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const isPalin = (num) => {
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if (numReverse(num) === num) {
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return true;
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}
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return false;
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};
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let total = 0;
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for (let i = 1; i < size; i++) {
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let loopCount = 1;
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let sum = i;
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while (loopCount < 50) {
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sum = sum + numReverse(sum);
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if (isPalin(sum)) {
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break;
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} else {
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loopCount++;
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}
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}
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if (loopCount === 50) {
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total++;
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}
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}
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return total;
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}
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```
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