1af6e7aa5a
* fix: clean-up Project Euler 321-340 * fix: typo * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
59 lines
2.3 KiB
Markdown
59 lines
2.3 KiB
Markdown
---
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id: 5900f4bd1000cf542c50ffcf
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title: 'Problem 336: Maximix Arrangements'
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challengeType: 5
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forumTopicId: 301994
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dashedName: problem-336-maximix-arrangements
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---
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# --description--
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A train is used to transport four carriages in the order: $ABCD$. However, sometimes when the train arrives to collect the carriages they are not in the correct order.
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To rearrange the carriages, they are all shunted onto a large rotating turntable. After the carriages are uncoupled at a specific point, the train moves off the turntable pulling the carriages still attached with it. The remaining carriages are rotated 180°. All of the carriages are then rejoined and this process is repeated as often as necessary in order to obtain the least number of uses of the turntable.
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Some arrangements, such as $ADCB$, can be solved easily: the carriages are separated between $A$ and $D$, and after $DCB$ are rotated the correct order has been achieved.
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However, Simple Simon, the train driver, is not known for his efficiency, so he always solves the problem by initially getting carriage $A$ in the correct place, then carriage $B$, and so on.
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Using four carriages, the worst possible arrangements for Simon, which we shall call maximix arrangements, are $DACB$ and $DBAC$; each requiring him five rotations (although, using the most efficient approach, they could be solved using just three rotations). The process he uses for $DACB$ is shown below.
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<img class="img-responsive center-block" alt="five rotations for maximix arrangement DACB" src="https://cdn.freecodecamp.org/curriculum/project-euler/maximix-arrangements.gif" style="background-color: white; padding: 10px;">
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It can be verified that there are 24 maximix arrangements for six carriages, of which the tenth lexicographic maximix arrangement is $DFAECB$.
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Find the ${2011}^{\text{th}}$ lexicographic maximix arrangement for eleven carriages.
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# --hints--
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`maximixArrangements()` should return a string.
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```js
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assert(typeof maximixArrangements() === 'string');
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```
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`maximixArrangements()` should return the string `CAGBIHEFJDK`.
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```js
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assert.strictEqual(maximixArrangements(), 'CAGBIHEFJDK');
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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 maximixArrangements() {
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return true;
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}
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maximixArrangements();
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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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