49 lines
1.0 KiB
Markdown
49 lines
1.0 KiB
Markdown
|
---
|
||
|
|
id: 5900f42f1000cf542c50ff40
|
||
|
|
title: 'Problem 194: Coloured Configurations'
|
||
|
|
challengeType: 5
|
||
|
|
forumTopicId: 301832
|
||
|
|
dashedName: problem-194-coloured-configurations
|
||
|
|
---
|
||
|
|
|
||
|
|
# --description--
|
||
|
|
|
||
|
|
Consider graphs built with the units A:
|
||
|
|
|
||
|
|
and B: , where the units are glued along
|
||
|
|
|
||
|
|
the vertical edges as in the graph .
|
||
|
|
|
||
|
|
A configuration of type (a,b,c) is a graph thus built of a units A and b units B, where the graph's vertices are coloured using up to c colours, so that no two adjacent vertices have the same colour. The compound graph above is an example of a configuration of type (2,2,6), in fact of type (2,2,c) for all c ≥ 4.
|
||
|
|
|
||
|
|
Let N(a,b,c) be the number of configurations of type (a,b,c). For example, N(1,0,3) = 24, N(0,2,4) = 92928 and N(2,2,3) = 20736.
|
||
|
|
|
||
|
|
Find the last 8 digits of N(25,75,1984).
|
||
|
|
|
||
|
|
# --hints--
|
||
|
|
|
||
|
|
`euler194()` should return 61190912.
|
||
|
|
|
||
|
|
```js
|
||
|
|
assert.strictEqual(euler194(), 61190912);
|
||
|
|
```
|
||
|
|
|
||
|
|
# --seed--
|
||
|
|
|
||
|
|
## --seed-contents--
|
||
|
|
|
||
|
|
```js
|
||
|
|
function euler194() {
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
euler194();
|
||
|
|
```
|
||
|
|
|
||
|
|
# --solutions--
|
||
|
|
|
||
|
|
```js
|
||
|
|
// solution required
|
||
|
|
```
|