--- 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 $n = 3$. three squares with red and blue counters placed on opposite ends of the row, separated by one empty square 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. allowed moves of the counter 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 ```