Question

What is the least number of straight lines needed to draw the following diagram?

• A. 39
• B. 40
• C. 42
• D. none of the above

Hint:

Count all horizontal lines, then all vertical lines, then all diagonal lines separately, treating each crossed line as one continuous line.

Answer 1

The Correct Option is A

Step 1: Set the counting rule.
Count a straight line as one single line for its whole length, even if other lines cross over it partway through. Do not double count a line just because something intersects it.

Step 2: Count the horizontal lines.
Going through the figure row by row and tracking every distinct horizontal line, including the short internal ones inside the nested rectangles, gives a total of 15 horizontal lines.

Step 3: Count the vertical lines.
Doing the same column by column, counting every distinct vertical line across the outer and inner rectangles, gives a total of 19 vertical lines.

Step 4: Count the inclined, diagonal, lines.
The figure has diagonal lines cutting across some of the rectangles, both the small inner square's diagonal and the diagonals in the side triangular shapes. Counting these gives a total of 5 inclined lines.

Step 5: Add them all up.
\( 15 + 19 + 5 = 39 \).

Final Answer:
The least number of straight lines needed is 39. \[ \boxed{39} \]