45 lines
903 B
Markdown
45 lines
903 B
Markdown
---
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id: 5900f4e61000cf542c50fff9
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title: 'Problem 378: Triangle Triples'
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challengeType: 5
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forumTopicId: 302040
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dashedName: problem-378-triangle-triples
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---
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# --description--
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Let $T(n)$ be the $n^{\text{th}}$ triangle number, so $T(n) = \frac{n(n + 1)}{2}$.
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Let $dT(n)$ be the number of divisors of $T(n)$. E.g.: $T(7) = 28$ and $dT(7) = 6$.
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Let $Tr(n)$ be the number of triples ($i$, $j$, $k$) such that $1 ≤ i < j < k ≤ n$ and $dT(i) > dT(j) > dT(k)$. $Tr(20) = 14$, $Tr(100) = 5\\,772$ and $Tr(1000) = 11\\,174\\,776$.
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Find $Tr(60\\,000\\,000)$. Give the last 18 digits of your answer.
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# --hints--
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`triangleTriples()` should return `147534623725724700`.
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```js
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assert.strictEqual(triangleTriples(), 147534623725724700);
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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 triangleTriples() {
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return true;
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}
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triangleTriples();
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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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