PASCAL 2022 Problem 21

A 5 \mathrm{~cm} by 5 \mathrm{~cm} pegboard and a 10 \mathrm{~cm} by 10 \mathrm{~cm} pegboard each have holes at the intersection of invisible horizontal and vertical lines that occur in 1 \mathrm{~cm} intervals from each edge. Pegs are placed into the holes on the two main diagonals of both pegboards. The 5 \mathrm{~cm} by 5 \mathrm{~cm} pegboard is shown; it has 16 holes. The 8 shaded holes have pegs, and the 8 unshaded holes do not. How many empty holes does the 10 \mathrm{~cm} by 10 \mathrm{~cm} pegboard have?

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