Question

Rep-tile is a shape that can be dissected into smaller copies of the same shape without leaving any remainder. For example a square can be cut into various numbers of smaller copies of square shape.
If no flip is allowed, which of the options is/are rep-tiles?

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is B, C, D

A rep-tile is a shape that can be dissected into smaller copies of itself without any remainder. No flipping is allowed, meaning the smaller shapes must maintain the same orientation as the original shape.

The task is to identify which of the given options can form smaller replicas of the original shape by simple division, maintaining the same orientation. Let's evaluate each figure. 

Figure 1 cannot be divided in a consistent manner where each section is a smaller, identical copy of the original shape. Hence, it is not a rep-tile.

Figure 2 can be consistently divided into smaller shapes identical to the original without overlap or gaps. Hence, it is a rep-tile.

Figure 3 can also be divided into smaller, identical shapes, meaning it satisfies the conditions of a rep-tile.

Figure 4 meets the criteria, as it can be divided into smaller copies of itself seamlessly and consistently. Hence, it too is a rep-tile.

In conclusion, Figures 2, 3, and 4 are rep-tiles as they can be dissected into smaller, identical copies without any remainder and without requiring them to be flipped.