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…

Question

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 xₙ. 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 x₄?

1. A. 16 (Correct answer)
2. B. 12
3. C. 8
4. D. 5

Correct Answer

Option A — 16

Detailed Solution & Explanation

The correct answer is Option A (16).

Key Points

• If the three cuts leave identical pieces, the cube is split into a small number of equal pieces (e.g. 4 slabs, or 8 small cubes by three perpendicular central cuts).
• The fourth cut is a single plane, so it can slice through only *some* of those pieces — it cannot cut every one of the eight small cubes at once.

Additional Information

• Because one plane cannot double the count from 8 to 16, x₄ = 16 is not achievable, while 12, 8 and 5 are reachable depending on the earlier configuration → Option A.