An organizer has 7777 chairs and wants a square arrangement (same number of rows and columns). What minimum number of chairs must be removed to form a perfect square layout?

Introduction:
To form a square layout, the total must be a perfect square. We remove the smallest possible number to reach the nearest perfect square not exceeding 7777.

Given Data / Assumptions:

• Total chairs = 7777

Concept / Approach:
Find k = floor(sqrt(7777)). Then k^2 is the nearest lower perfect square. The minimum removal is 7777 − k^2.

Step-by-Step Solution:
k = floor(sqrt(7777)) = 88k^2 = 88^2 = 7744Minimum removal = 7777 − 7744 = 33

Verification / Alternative check:
The next higher square is 89^2 = 7921, which would require adding chairs, not removing.

Why Other Options Are Wrong:
25, 44, 121 do not equal 7777 − 7744.

Common Pitfalls:
Rounding sqrt upward; attempting to remove to the nearest higher square rather than lower.

Final Answer:
33