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.