1.8 KiB
1.8 KiB
id | challengeType | title |
---|---|---|
5900f4be1000cf542c50ffd1 | 5 | Problem 338: Cutting Rectangular Grid Paper |
Description
Similarly, from a sheet with dimensions 9 × 8 , we can make rectangles with dimensions 18 × 4 and 12 × 6 .
For a pair w and h, let F(w,h) be the number of distinct rectangles that can be made from a sheet with dimensions w × h . For example, F(2,1) = 0, F(2,2) = 1, F(9,4) = 3 and F(9,8) = 2. Note that rectangles congruent to the initial one are not counted in F(w,h). Note also that rectangles with dimensions w × h and dimensions h × w are not considered distinct.
For an integer N, let G(N) be the sum of F(w,h) for all pairs w and h which satisfy 0 < h ≤ w ≤ N. We can verify that G(10) = 55, G(103) = 971745 and G(105) = 9992617687.
Find G(1012). Give your answer modulo 108.
Instructions
Tests
tests:
- text: <code>euler338()</code> should return 15614292.
testString: assert.strictEqual(euler338(), 15614292, '<code>euler338()</code> should return 15614292.');
Challenge Seed
function euler338() {
// Good luck!
return true;
}
euler338();
Solution
// solution required