152 lines
3.4 KiB
Markdown
152 lines
3.4 KiB
Markdown
---
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id: 5ea2815a8640bcc6cb7dab3c
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title: Lychrel numbers
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challengeType: 5
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forumTopicId: 385287
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dashedName: lychrel-numbers
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---
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# --description--
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<ol>
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<li>Take an integer <code>n₀</code>, greater than zero.</li>
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<li>Form the next number <code>n</code> of the series by reversing <code>n₀</code> and adding it to <code>n₀</code></li>
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<li>Stop when <code>n</code> becomes palindromic - i.e. the digits of <code>n</code> in reverse order == <code>n</code>.</li>
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</ol>
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The above recurrence relation when applied to most starting numbers `n` = 1, 2, ... terminates in a palindrome quite quickly.
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For example if `n₀` = 12 we get:
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```bash
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12
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12 + 21 = 33, a palindrome!
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```
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And if `n₀` = 55 we get:
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```bash
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55
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55 + 55 = 110
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110 + 011 = 121, a palindrome!
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```
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Notice that the check for a palindrome happens *after* an addition.
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Some starting numbers seem to go on forever; the recurrence relation for 196 has been calculated for millions of repetitions forming numbers with millions of digits, without forming a palindrome. These numbers that do not end in a palindrome are called **Lychrel numbers**.
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For the purposes of this task a Lychrel number is any starting number that does not form a palindrome within 500 (or more) iterations.
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**Seed and related Lychrel numbers:**
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Any integer produced in the sequence of a Lychrel number is also a Lychrel number.
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In general, any sequence from one Lychrel number *might* converge to join the sequence from a prior Lychrel number candidate; for example the sequences for the numbers 196 and then 689 begin:
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```bash
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196
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196 + 691 = 887
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887 + 788 = 1675
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1675 + 5761 = 7436
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7436 + 6347 = 13783
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13783 + 38731 = 52514
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52514 + 41525 = 94039
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...
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689
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689 + 986 = 1675
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1675 + 5761 = 7436
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...
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```
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So we see that the sequence starting with 689 converges to, and continues with the same numbers as that for 196.
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Because of this we can further split the Lychrel numbers into true **Seed** Lychrel number candidates, and **Related** numbers that produce no palindromes but have integers in their sequence seen as part of the sequence generated from a lower Lychrel number.
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# --instructions--
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Write a function that takes a number as a parameter. Return true if the number is a Lynchrel number. Otherwise, return false. Remember that the iteration limit is 500.
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# --hints--
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`isLychrel` should be a function.
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```js
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assert(typeof isLychrel === 'function');
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```
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`isLychrel(12)` should return a boolean.
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```js
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assert(typeof isLychrel(12) === 'boolean');
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```
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`isLychrel(12)` should return `false`.
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```js
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assert.equal(isLychrel(12), false);
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```
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`isLychrel(55)` should return `false`.
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```js
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assert.equal(isLychrel(55), false);
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```
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`isLychrel(196)` should return `true`.
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```js
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assert.equal(isLychrel(196), true);
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```
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`isLychrel(879)` should return `true`.
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```js
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assert.equal(isLychrel(879), true);
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```
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`isLychrel(44987)` should return `false`.
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```js
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assert.equal(isLychrel(44987), false);
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```
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`isLychrel(7059)` should return `true`.
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```js
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assert.equal(isLychrel(7059), true);
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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 isLychrel(n) {
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}
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```
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# --solutions--
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```js
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function isLychrel(n) {
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function reverse(num) {
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return parseInt(
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num
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.toString()
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.split('')
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.reverse()
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.join('')
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);
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}
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var i;
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for (i = 0; i < 500; i++) {
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n = n + reverse(n);
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if (n == reverse(n)) break;
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}
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return i == 500;
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}
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```
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