How to turn 1 red into 3 red: r--R-->bg--G-->rbb--B-->rrgb--R-1-->rrr How to turn 1 red into 5 red in 6 steps: r--R-->bg--G-->rbb--B-->rrgrg--G-->rrrrbb--B-->rrrrrrgg--R-->rrrrrgggb Cannot convert one red brick into five in less than six moves because an R+ is the only valid move in the beginning which reduces the amount of red bricks. This means that for each of our moves, we need to increase the number of red bricks. Seeming as we can, on average add one per move (more requires setup moves), we must take, at minimum, six moves (number of bricks + 1 required move)