61 lines
1.4 KiB
Markdown
61 lines
1.4 KiB
Markdown
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---
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id: 5900f4771000cf542c50ff8a
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challengeType: 5
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title: 'Problem 267: Billionaire'
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---
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## Description
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<section id='description'>
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You are given a unique investment opportunity.
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Starting with £1 of capital, you can choose a fixed proportion, f, of your capital to bet on a fair coin toss repeatedly for 1000 tosses.
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Your return is double your bet for heads and you lose your bet for tails.
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For example, if f = 1/4, for the first toss you bet £0.25, and if heads comes up you win £0.5 and so then have £1.5. You then bet £0.375 and if the second toss is tails, you have £1.125.
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Choosing f to maximize your chances of having at least £1,000,000,000 after 1,000 flips, what is the chance that you become a billionaire?
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All computations are assumed to be exact (no rounding), but give your answer rounded to 12 digits behind the decimal point in the form 0.abcdefghijkl.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler267()</code> should return 0.999992836187.
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testString: 'assert.strictEqual(euler267(), 0.999992836187, ''<code>euler267()</code> should return 0.999992836187.'');'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler267() {
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// Good luck!
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return true;
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}
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euler267();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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