ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
51 lines
1.4 KiB
Markdown
51 lines
1.4 KiB
Markdown
---
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id: 5900f4971000cf542c50ffaa
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title: 'Problem 299: Three similar triangles'
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challengeType: 5
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forumTopicId: 301951
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dashedName: problem-299-three-similar-triangles
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---
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# --description--
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Four points with integer coordinates are selected:A(a, 0), B(b, 0), C(0, c) and D(0, d),
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with 0 < a < b and 0 < c < d.
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Point P, also with integer coordinates, is chosen on the line AC so that the three triangles ABP, CDP and BDP are all similar.
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It is easy to prove that the three triangles can be similar, only if a=c.
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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.
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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.
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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?
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# --hints--
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`euler299()` should return 549936643.
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```js
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assert.strictEqual(euler299(), 549936643);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler299() {
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return true;
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}
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euler299();
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```
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# --solutions--
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```js
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// solution required
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```
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