49 lines
1.2 KiB
Markdown
49 lines
1.2 KiB
Markdown
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---
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id: 5900f3dd1000cf542c50feef
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title: 'Problem 112: Bouncy numbers'
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challengeType: 5
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forumTopicId: 301738
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dashedName: problem-112-bouncy-numbers
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---
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# --description--
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Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.
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Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.
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We shall call a positive integer that is neither increasing nor decreasing a "bouncy" number; for example, 155349.
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Clearly there cannot be any bouncy numbers below one-hundred, but just over half of the numbers below one-thousand (525) are bouncy. In fact, the least number for which the proportion of bouncy numbers first reaches 50% is 538.
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Surprisingly, bouncy numbers become more and more common and by the time we reach 21780 the proportion of bouncy numbers is equal to 90%.
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Find the least number for which the proportion of bouncy numbers is exactly 99%.
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# --hints--
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`euler112()` should return 1587000.
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```js
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assert.strictEqual(euler112(), 1587000);
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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 euler112() {
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return true;
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}
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euler112();
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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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