Balancing Colored Points on a Line by Exchanging Intervals
Atsushi Kaneko, Mikio Kanō, Mamoru Watanabe · Journal of Information Processing · 2017
Assume that 2a red points, 2b blue points and 2c green points lie on a line, and they are bisected into a left part I and a right part J by a point so that each of them contains a + b + c points.Then we show that there exist a point set X ⊂ I and a point set Y ⊂ J such that both X and Y consist of consecutive points, |X| = |Y|, and each of I -X + Y and J -Y + X contains exactly a red points, b blue points and c green points.Moreover we extend this result to multi-colored point sets.