---
id: 5900f4ae1000cf542c50ffc0
title: 'Problem 321: Swapping Counters'
challengeType: 5
forumTopicId: 301978
dashedName: problem-321-swapping-counters
---
# --description--
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 $n = 3$.
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.
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.
It can be verified $M(3) = 15$, which also happens to be a triangle number.
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.
Find the sum of the first forty terms of this sequence.
# --hints--
`swappingCounters()` should return `2470433131948040`.
```js
assert.strictEqual(swappingCounters(), 2470433131948040);
```
# --seed--
## --seed-contents--
```js
function swappingCounters() {
return true;
}
swappingCounters();
```
# --solutions--
```js
// solution required
```