47 lines
1.3 KiB
Markdown
47 lines
1.3 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 centre. For example, when n = 3.
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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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Let M(n) represent the minimum number of moves/actions to completely reverse the positions of the coloured counters; that is, move all the red counters to the right and all the blue counters to the left. 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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`euler321()` should return 2470433131948040.
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```js
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assert.strictEqual(euler321(), 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 euler321() {
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return true;
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}
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euler321();
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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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