48 lines
925 B
Markdown
48 lines
925 B
Markdown
---
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id: 5900f4931000cf542c50ffa5
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title: 'Problem 294: Sum of digits - experience #23'
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challengeType: 5
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forumTopicId: 301946
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dashedName: problem-294-sum-of-digits---experience-23
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---
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# --description--
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For a positive integer $k$, define $d(k)$ as the sum of the digits of $k$ in its usual decimal representation. Thus $d(42) = 4 + 2 = 6$.
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For a positive integer $n$, define $S(n)$ as the number of positive integers $k < {10}^n$ with the following properties:
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- $k$ is divisible by 23 and,
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- $d(k) = 23$.
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You are given that $S(9) = 263\\,626$ and $S(42) = 6\\,377\\,168\\,878\\,570\\,056$.
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Find $S({11}^{12})$ and give your answer $\bmod {10}^9$.
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# --hints--
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`experience23()` should return `789184709`.
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```js
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assert.strictEqual(experience23(), 789184709);
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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 experience23() {
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return true;
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}
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experience23();
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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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