2.1 KiB
2.1 KiB
id | challengeType | title |
---|---|---|
5900f51f1000cf542c510031 | 5 | Problem 434: Rigid graphs |
Description
The grid graphs embedded in the Euclidean plane are not rigid, as the following animation demonstrates: However, one can make them rigid by adding diagonal edges to the cells. For example, for the 2x3 grid graph, there are 19 ways to make the graph rigid: Note that for the purposes of this problem, we do not consider changing the orientation of a diagonal edge or adding both diagonal edges to a cell as a different way of making a grid graph rigid.
Let R(m,n) be the number of ways to make the m × n grid graph rigid. E.g. R(2,3) = 19 and R(5,5) = 23679901
Define S(N) as ∑R(i,j) for 1 ≤ i, j ≤ N. E.g. S(5) = 25021721. Find S(100), give your answer modulo 1000000033
Instructions
Tests
tests:
- text: <code>euler434()</code> should return 863253606.
testString: 'assert.strictEqual(euler434(), 863253606, ''<code>euler434()</code> should return 863253606.'');'
Challenge Seed
function euler434() {
// Good luck!
return true;
}
euler434();
Solution
// solution required