Private room available is the twenty-ninth level of the Present difficulty in the Genesis/Mega Drive port of Lemmings and the third level of SUNSOFT in the Super NES port of Lemmings as SUNSOFT SPECIAL 3.
Strategy[]
The title refers to the 18 rooms where you can store a Lemming, and dig to leave. You can only assign one lemming to one room, so that they can dig out of the room and safely descend to the floor. If you put two lemmings in the same room, one will splat when the first one who digs. There will be two lemmings remaining, who need to use an alternate strategy to safely descend to the floor.
Experiment with digging through the top floor to the level of the rooms. See if lemming #2 turns to the left, while lemming #1 digs. If so, assign lemming #2 to the far left room. Assign lemming #1 to the far right, and continue to the left with each subsequent lemming.
Lemmings 19 and 20 will need an alternate location to dig. Use the icicles to assist the two diggers, and aim the digger to the side of the icicle near the high side of the crystal below. While lemmings 19 and 20 are still digging, release the lemming in the far left room while walking to the left, careful not to release his neighbor. This lemming will do the trailblazer work, dig/bash out beneath the metal. Lemmings 19 and 20 will take their time to walk to the far right, and turn around, while the trailblazer does the work. The trailblazer will build across the gap, and bash through the crystal to get to the exit. Release the remaining lemmings from their private rooms.