--- id: 5900f5191000cf542c51002b challengeType: 5 title: 'Problem 428: Necklace of Circles' forumTopicId: 302098 --- ## Description
Let a, b and c be positive numbers. Let W, X, Y, Z be four collinear points where |WX| = a, |XY| = b, |YZ| = c and |WZ| = a + b + c. Let Cin be the circle having the diameter XY. Let Cout be the circle having the diameter WZ. The triplet (a, b, c) is called a necklace triplet if you can place k ≥ 3 distinct circles C1, C2, ..., Ck such that: For example, (5, 5, 5) and (4, 3, 21) are necklace triplets, while it can be shown that (2, 2, 5) is not. a visual reresentation of a necklace triplet Let T(n) be the number of necklace triplets (a, b, c) such that a, b and c are positive integers, and bn. For example, T(1) = 9, T(20) = 732 and T(3000) = 438106. Find T(1 000 000 000).
## Instructions
## Tests
```yml tests: - text: necklace(1000000000) should return 747215561862. testString: assert.strictEqual(necklace(1000000000), 747215561862); ```
## Challenge Seed
```js function necklace(n) { // Good luck! return true; } necklace(1000000000) ```
## Solution
```js // solution required ```