1.7 KiB
1.7 KiB
id | challengeType | title |
---|---|---|
5900f4971000cf542c50ffaa | 5 | Problem 299: Three similar triangles |
Description
It is easy to prove that the three triangles can be similar, only if a=c.
So, given that a=c, we are looking for triplets (a,b,d) such that at least one point P (with integer coordinates) exists on AC, making the three triangles ABP, CDP and BDP all similar.
For example, if (a,b,d)=(2,3,4), it can be easily verified that point P(1,1) satisfies the above condition. Note that the triplets (2,3,4) and (2,4,3) are considered as distinct, although point P(1,1) is common for both.
If b+d < 100, there are 92 distinct triplets (a,b,d) such that point P exists. If b+d < 100 000, there are 320471 distinct triplets (a,b,d) such that point P exists. If b+d < 100 000 000, how many distinct triplets (a,b,d) are there such that point P exists?
Instructions
Tests
tests:
- text: <code>euler299()</code> should return 549936643.
testString: assert.strictEqual(euler299(), 549936643, '<code>euler299()</code> should return 549936643.');
Challenge Seed
function euler299() {
// Good luck!
return true;
}
euler299();
Solution
// solution required