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>
53 lines
1.8 KiB
Markdown
53 lines
1.8 KiB
Markdown
---
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id: 5900f4ae1000cf542c50ffc0
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title: 'Problem 321: Swapping Counters'
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challengeType: 5
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forumTopicId: 301978
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dashedName: problem-321-swapping-counters
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---
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# --description--
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A horizontal row comprising of $2n + 1$ squares has $n$ red counters placed at one end and $n$ blue counters at the other end, being separated by a single empty square in the center. For example, when $n = 3$.
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<img class="img-responsive center-block" alt="three squares with red and blue counters placed on opposite ends of the row, separated by one empty square" src="https://cdn.freecodecamp.org/curriculum/project-euler/swapping-counters-1.gif" style="background-color: white; padding: 10px;">
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A counter can move from one square to the next (slide) or can jump over another counter (hop) as long as the square next to that counter is unoccupied.
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<img class="img-responsive center-block" alt="allowed moves of the counter" src="https://cdn.freecodecamp.org/curriculum/project-euler/swapping-counters-2.gif" style="background-color: white; padding: 10px;">
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Let $M(n)$ represent the minimum number of moves/actions to completely reverse the positions of the colored counters; that is, move all the red counters to the right and all the blue counters to the left.
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It can be verified $M(3) = 15$, which also happens to be a triangle number.
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If we create a sequence based on the values of n for which $M(n)$ is a triangle number then the first five terms would be: 1, 3, 10, 22, and 63, and their sum would be 99.
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Find the sum of the first forty terms of this sequence.
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# --hints--
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`swappingCounters()` should return `2470433131948040`.
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```js
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assert.strictEqual(swappingCounters(), 2470433131948040);
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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 swappingCounters() {
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return true;
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}
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swappingCounters();
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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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