66 lines
1.5 KiB
Markdown
66 lines
1.5 KiB
Markdown
---
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id: 5900f5101000cf542c510022
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title: 'Problem 419: Look and say sequence'
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challengeType: 5
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forumTopicId: 302088
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dashedName: problem-419-look-and-say-sequence
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---
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# --description--
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The look and say sequence goes 1, 11, 21, 1211, 111221, 312211, 13112221, 1113213211, ...
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The sequence starts with 1 and all other members are obtained by describing the previous member in terms of consecutive digits.
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It helps to do this out loud:
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1 is 'one one' $→ 11$
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11 is 'two ones' $→ 21$
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21 is 'one two and one one' $→ 1211$
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1211 is 'one one, one two and two ones' $→ 111221$
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111221 is 'three ones, two twos and one one' $→ 312211$
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...
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Define $A(n)$, $B(n)$ and $C(n)$ as the number of ones, twos and threes in the $n$'th element of the sequence respectively. One can verify that $A(40) = 31\\,254$, $B(40) = 20\\,259$ and $C(40) = 11\\,625$.
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Find $A(n)$, $B(n)$ and $C(n)$ for $n = {10}^{12}$. Give your answer modulo $2^{30}$ as a string and separate your values for $A$, $B$ and $C$ by a comma. E.g. for $n = 40$ the answer would be `31254,20259,11625`.
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# --hints--
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`lookAndSaySequence()` should return a string.
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```js
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assert(typeof lookAndSaySequence() === 'string');
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```
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`lookAndSaySequence()` should return the string `998567458,1046245404,43363922`.
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```js
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assert.strictEqual(lookAndSaySequence(), '998567458,1046245404,43363922');
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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 lookAndSaySequence() {
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return true;
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}
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lookAndSaySequence();
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```
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# --solutions--
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```js
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// solution required
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```
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