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---
title: 9 billion names of God the integer
id: 5949b579404977fbaefcd736
challengeType: 5
---
## Description
< section id = 'description' >
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This task is a variation of the < a href = 'https://en.wikipedia.org/wiki/The Nine Billion Names of God#Plot_summary' title = 'wp: The Nine Billion Names of God#Plot_summary' target = '_blank' > short story by Arthur C. Clarke< / a > .
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(Solvers should be aware of the consequences of completing this task.)
In detail, to specify what is meant by a “name”:
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< ul >
< li > The integer 1 has 1 name “1”.< / li >
< li > The integer 2 has 2 names “1+1”, and “2”.< / li >
< li > The integer 3 has 3 names “1+1+1”, “2+1”, and “3”.< / li >
< li > The integer 4 has 5 names “1+1+1+1”, “2+1+1”, “2+2”, “3+1”, “4”.< / li >
< li > The integer 5 has 7 names “1+1+1+1+1”, “2+1+1+1”, “2+2+1”, “3+1+1”, “3+2”, “4+1”, “5”.< / li >
< / ul >
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This can be visualized in the following form:
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< pre >
1
1 1
1 1 1
1 2 1 1
1 2 2 1 1
1 3 3 2 1 1
< / pre >
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Where row $n$ corresponds to integer $n$, and each column $C$ in row $m$ from left to right corresponds to the number of names beginning with $C$.
Optionally note that the sum of the $n$-th row $P(n)$ is the < a href = "http://mathworld.wolfram.com/PartitionFunctionP.html" title = "link: http://mathworld.wolfram.com/PartitionFunctionP.html" > integer partition function< / a > .
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< / section >
## Instructions
< section id = 'instructions' >
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Implement a function that returns the sum of the $n$-th row.
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< / section >
## Tests
< section id = 'tests' >
```yml
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tests:
- text: < code > numberOfNames</ code > is a function.
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testString: assert(typeof numberOfNames === 'function', '< code > numberOfNames< / code > is a function.');
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- text: < code > numberOfNames(5)</ code > should equal 7.
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testString: assert.equal(numberOfNames(5), 7, '< code > numberOfNames(5)< / code > should equal 7.');
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- text: < code > numberOfNames(12)</ code > should equal 77.
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testString: assert.equal(numberOfNames(12), 77, '< code > numberOfNames(12)< / code > should equal 77.');
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- text: < code > numberOfNames(18)</ code > should equal 385.
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testString: assert.equal(numberOfNames(18), 385, '< code > numberOfNames(18)< / code > should equal 385.');
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- text: < code > numberOfNames(23)</ code > should equal 1255.
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testString: assert.equal(numberOfNames(23), 1255, '< code > numberOfNames(23)< / code > should equal 1255.');
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- text: < code > numberOfNames(42)</ code > should equal 53174.
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testString: assert.equal(numberOfNames(42), 53174, '< code > numberOfNames(42)< / code > should equal 53174.');
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- text: < code > numberOfNames(123)</ code > should equal 2552338241.
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testString: assert.equal(numberOfNames(123), 2552338241, '< code > numberOfNames(123)< / code > should equal 2552338241.');
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```
< / section >
## Challenge Seed
< section id = 'challengeSeed' >
< div id = 'js-seed' >
```js
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function numberOfNames(num) {
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// Good luck!
return true;
}
```
< / div >
< / section >
## Solution
< section id = 'solution' >
```js
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function numberOfNames(num) {
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const cache = [
[1]
];
for (let l = cache.length; l < num + 1 ; l + + ) {
let Aa;
let Mi;
const r = [0];
for (let x = 1; x < l + 1 ; x + + ) {
r.push(r[r.length - 1] + (Aa = cache[l - x < 0 ? cache . length - ( l - x ) : l - x ] ) [ ( Mi = Math.min(x, l - x ) ) < 0 ? Aa . length - Mi : Mi ] ) ;
}
cache.push(r);
}
return cache[num][cache[num].length - 1];
}
```
< / section >