The number of pennies on square 33 is the sum of ALL the pennies on the first half of the chess board.

With the usual doubling pattern, square 1 has 1 penny and each square has twice as many as the one before it. The total on squares 1 through 32 is 1 + 2 + 4 + … + 2³¹ = 2³² − 1, while square 33 has 2³² pennies. So the number on square 33 is greater than the total on the first half of the board.

AI-written and checked against the verified answer.