Mario moves on to find a way to get through the main gates of Bowser’s chamber. He suddenly finds falling through a trapdoor and lands on something hard. The Devil Ghost Banshee , comes out and says, “This room is a standard 8×8 chessboard. Each of its 64 square is assigned a weight. These weights are assigned in such a manner that weight of a square is an average of the weight of the square that it is surrounded by.” Mario now has to determine the weights of all 64 squares and for that Banshee tells him the weights of X squares. What could be the minimum value of X with which Mario can deduce the weights of every other square?

Options

A. 8
B. 32
C. 56
D. None of these

Explanation

To determine the minimum number of squares (X) that the Banshee must tell Mario in order to deduce the weights of all 64 squares on the chessboard, let’s analyze the situation step by step.

### Step 1: Understanding the Chessboard Configuration
The chessboard is an 8×8 grid, which means it has a total of 64 squares. Each square has a weight, and the weight of a square is defined as the average of the weights of the squares that surround it.

### Step 2: Analyzing the Weight Calculation
For a square located in the interior of the chessboard (not on the edge), it is surrounded by 8 other squares. The weight of that square is the average of those 8 surrounding weights. For edge squares, they are surrounded by fewer squares (5 or 6), and corner squares are surrounded by only 3 squares.

...