2018-09-30 22:01:58 +00:00
---
id: 5900f42f1000cf542c50ff40
title: 'Problem 194: Coloured Configurations'
2020-11-27 18:02:05 +00:00
challengeType: 5
2019-08-05 16:17:33 +00:00
forumTopicId: 301832
2021-01-13 02:31:00 +00:00
dashedName: problem-194-coloured-configurations
2018-09-30 22:01:58 +00:00
---
2020-11-27 18:02:05 +00:00
# --description--
2018-10-08 00:01:53 +00:00
Consider graphs built with the units A:
2020-11-27 18:02:05 +00:00
2018-09-30 22:01:58 +00:00
and B: , where the units are glued along
2020-11-27 18:02:05 +00:00
2018-09-30 22:01:58 +00:00
the vertical edges as in the graph .
2020-11-27 18:02:05 +00:00
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.
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
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.
2018-09-30 22:01:58 +00:00
Find the last 8 digits of N(25,75,1984).
2020-11-27 18:02:05 +00:00
# --hints--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
`euler194()` should return 61190912.
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
```js
assert.strictEqual(euler194(), 61190912);
2018-09-30 22:01:58 +00:00
```
2020-11-27 18:02:05 +00:00
# --seed--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
## --seed-contents--
2018-09-30 22:01:58 +00:00
```js
function euler194() {
2020-09-15 16:57:40 +00:00
2018-09-30 22:01:58 +00:00
return true;
}
euler194();
```
2020-11-27 18:02:05 +00:00
# --solutions--
2018-09-30 22:01:58 +00:00
```js
// solution required
```
