Question

Four cut-outs of shapes (labelled \(\,p, q, r, s\,\)) are shown. Using one or more cut-out pieces, how many unique combinations can make a square/rectangle? (Different combinations of pieces count as different, even if the final rectangle looks the same. Rotations/reflections of the same piece-combination count as one.)

• A. 4
• B. 5
• C. 6
• D. 3

Hint:

When a puzzle says “unique combinations,” count which pieces are used—not just the final outline. Rotations and reflections of the same set count as one.

Answer 1

The Correct Option is B

Step 1: Read the uniqueness rule carefully.
Two results are the same if they use the same set of pieces (even in different orientations). Results are different if they use different combinations of pieces, even if the final rectangle is identical in shape/size.
Step 2: Identify which single pieces already form rectangles.
- \(\,q\,\) is a rectangle on its own ⇒ one combination.
- \(\,s\,\) is also a rectangle on its own ⇒ one combination.
Thus, singles give: \(\{q\}\) and \(\{s\}\) ⇒ \(2\) unique combinations so far.
Step 3: Identify pairs of pieces that can complete into rectangles.
From the provided hints/figures:
- \(\,p + p\,\) can pair (two mirror slants) to make a rectangle ⇒ \(+1\).
- \(\,r + r\,\) can pair similarly to make a rectangle ⇒ \(+1\).
- \(\,p + r\,\) can combine to form a rectangle; the sheet explicitly shows a rectangle labelled \(\,p,r\,\) and notes it is a different combination from using \(s\) alone even if identical in outline ⇒ \(+1\).
Step 4: Tally unique combinations.
\(\{q\}, \{s\}, \{p+p\}, \{r+r\}, \{p+r\} ⇒ 5\) unique rectangle-making combinations. Final Answer: \[ \boxed{\text{(B) } 5} \]