1.5 KiB
1.5 KiB
id | challengeType | title |
---|---|---|
5900f4931000cf542c50ffa6 | 5 | Problem 295: Lenticular holes |
Description
Consider the circles: C0: x2+y2=25 C1: (x+4)2+(y-4)2=1 C2: (x-12)2+(y-4)2=65
The circles C0, C1 and C2 are drawn in the picture below.
C0 and C1 form a lenticular hole, as well as C0 and C2.
We call an ordered pair of positive real numbers (r1, r2) a lenticular pair if there exist two circles with radii r1 and r2 that form a lenticular hole. We can verify that (1, 5) and (5, √65) are the lenticular pairs of the example above.
Let L(N) be the number of distinct lenticular pairs (r1, r2) for which 0 < r1 ≤ r2 ≤ N. We can verify that L(10) = 30 and L(100) = 3442.
Find L(100 000).
Instructions
Tests
tests:
- text: <code>euler295()</code> should return 4884650818.
testString: assert.strictEqual(euler295(), 4884650818, '<code>euler295()</code> should return 4884650818.');
Challenge Seed
function euler295() {
// Good luck!
return true;
}
euler295();
Solution
// solution required