Question

Three views of a stack of sugar cubes are shown below. What is the \textbf{MINIMUM number of cubes that are required to produce this stack?}

• A. A
• B. B
• C. C
• D. D

Hint:

For minimum-cube 3D view problems: \begin{itemize} \item Use the top view to count columns, \item Use front and side views to determine column heights, \item Always take the minimum compatible height for each column. \end{itemize}

Answer 1

The Correct Option is A

Step 1: From the top view, we observe a full \(4 \times 4\) grid. This means there are \(16\) vertical columns in total. \bigskip Step 2: The front view shows column heights increasing stepwise from left to right as: \[ 1,\; 2,\; 3,\; 4 \] \bigskip Step 3: The side view shows the same stepped height pattern: \[ 1,\; 2,\; 3,\; 4 \] \bigskip Step 4: To obtain the \emph{minimum} number of cubes, each vertical column must have a height equal to the minimum height allowed by both the front and side views. Thus, the height matrix is: \[ \begin{matrix} 1 & 1 & 1 & 1
1 & 2 & 2 & 2
1 & 2 & 3 & 3
1 & 2 & 3 & 4 \end{matrix} \] \bigskip Step 5: Sum of all column heights: \[ (4\times1) + (3\times2 + 1\times1) + (2\times3 + 2\times2) + (1\times4 + 1\times3 + 1\times2 + 1\times1) = 25 \] \bigskip Final Answer: \[ \boxed{25} \] \bigskip