12. (12 points) A row of 2012 balls, colored red, yellow, and blue, are arranged in a line, with a distance of 1 centimeter between each adjacent pair of balls. In every set of 4 adjacent balls, there is 1 red ball, 1 yellow ball, and 2 blue balls. The distance between the 100th red ball from the left and the 100th yellow ball from the right is 1213 centimeters. The distance between the 100th blue ball from the left and the 100th blue ball from the right is $\qquad$ centimeters.
【Solution】Solution: According to the analysis, every 4 balls include 1 red ball and 1 yellow ball, so the 100th red ball from the left should be in $(3979, 398, 399, 400)$;

The 100th yellow ball from the right should be in $(1613,1614,1615,1616)$, since the distance between the two balls is 1213 cm, it can only be 400 and 1613, meaning the 400th ball is red and the 1613th ball is yellow, so starting from the first ball, the colors of the balls cycle as “yellow, blue, blue, red”,

The 100th blue ball from the left should be the 199th in $(197,198,199,200)$, and the 100th blue ball from the right should be the 1814th in $(1813,1814,1815,1816)$, the distance between them is $1814-199=1615$ cm. Therefore, the answer is: 1615.