Question

Three views of a block with seven different shapes printed on its faces are shown. Find the same block from the options.

• A. A
• B. B
• C. C
• D. D

Hint:

For “find the solid” problems, write an adjacency table from each view (what is seen together shares an edge). Intersect the tables and discard any option that breaks a required neighbour pair.

Answer 1

The Correct Option is A

Label the seven symbols as: \(\boxed{\square}\) (hollow square), \(\boxed{\circ}\) (circle), \(\boxed{\triangle}\) (triangle), \(\boxed{\star}\) (star), a long \(\boxed{\rule{8mm}{1.2pt}}\) rectangle, a \(\boxed{\scriptsize\blacksquare}\) on the top face (small filled square), and the \(\boxed{\text{Z}}\) (lightning/zig-zag). We will deduce adjacencies from the three orthographic views and then eliminate options.
Adjacency facts from the three views
\(\bullet\) View 1: faces seen together are \(\text{Z}\) (top), \(\square\) and \(\circ\). Hence \(\square\) is adjacent to both \(\text{Z}\) and \(\circ\).
\(\bullet\) View 2: faces seen are again \(\text{Z}\) (top), the long rectangle, and \(\triangle\). Therefore the long rectangle and \(\triangle\) are each adjacent to \(\text{Z}\); also \(\square\) is not opposite the long rectangle (since they appear with the same top in V1/V2).
\(\bullet\) View 3: the top shows the small filled \(\blacksquare\); the visible sides are \(\star\) and \(\circ\). So \(\blacksquare\) is adjacent to \(\star\) and \(\circ\). Collecting the constraints
Around the \(\square\) (seen prominently in V1/V2) the neighbours we have evidence for are \[ \{\text{Z},\ \circ,\ \triangle,\ \text{long rectangle}\}. \] Also, \(\blacksquare\) must be adjacent to \(\{\star,\ \circ\}\) (from V3). Any correct option must place these pairs on meeting faces and avoid placing any pair that was never seen together (e.g., \(\star\) with \(\triangle\)) on opposite sides erroneously. Check the options
(A) satisfies all the above simultanously: \(\square\) meets \(\circ\) and the long rectangle on adjoining faces and is reachable from the \(\text{Z}\) face as in the given views; the \(\blacksquare\) top has \(\star\) and \(\circ\) as neighbours exactly as in V3.
(B), (C) and (D) each violate at least one adjacency: one of them places \(\triangle\) opposite the long rectangle (contradicting V2), another separates \(\blacksquare\) from \(\star\) (contradicting V3), and another does not allow \(\square\) to be adjacent to both \(\circ\) and \(\text{Z}\) (contradicting V1).
Hence the only consistent solid is \(\boxed{(A)}\).