Question

$1024$ plants are planted in a grid such that the number of rows is equal to the number of columns. One row and one column of plants are then sold to a customer. Find the number of plants that were sold.

• A. $61$
• B. $65$
• C. $63$
• D. $67$

Answer 1

The correct option is C $63$

Number of trees $=1024$
Since the number of rows is equal to the number of columns, it implies that the number of plants is a perfect square.
Therefore, number of rows (or number of columns) $=$ square root of $1024$ (number of plants)
$=\sqrt{1024}$
$=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2}$
$=2\times 2\times 2\times 2\times 2$
$=32$
Therefore, initial number of rows (or columns) $=32$
After 1 row and 1 column of plants are sold,
Number of rows (or columns) $=32-1=31$
Number of plants remaining $={31}^2$
Therefore, the number of plants sold $={32}^2-{31}^2$
$=1024-961$
$=63$