A cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total number of pieces produced by applying n cuts is denoted by x_n. The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for x_4?

After 3 cuts giving identical pieces with the cube unmoved, possible scenarios: (a) 3 mutually perpendicular cuts → 8 identical small cubes. (b) 3 parallel cuts → 4 identical slabs (but this gives 4 not identical with constraints, so consider). For x_4 (the 4th cut on the 8-piece configuration): one cut through all 8 cubes can produce up to 16 pieces (if cut passes through all 8). Cutting through fewer pieces gives values like 8+k where k = number of pieces actually cut. For 3 parallel cuts giving 4 identical slabs, the 4th cut can give various values. Possible x_4 values include 16 (cut through all 8), 12 (cut through 4), 8 (cut through 0 additional but rearranges — actually adds pieces equal to count cut). Value 5 is not achievable since each cut adds at least 1 piece to the count of pieces it passes through, and starting from 8 pieces, x_4 ≥ 9, or starting from 4 pieces (parallel cut config) x_4 ≥ 5 but with specific constraints making 5 impossible.