2025 AMC 10B Problem 23

A rectangular grid of squares has 141 rows and 91 columns. Each square has room for two numbers. Horace and Vera each fill in the grid by putting the numbers from 1 through 141 \times 91 = 12{,}831 into the squares. Horace fills the grid horizontally: he puts 1 through 91 in order from left to right into row 1, puts 92 through 182 into row 2 in order from left to right, and continues similarly through row 141. Vera fills the grid vertically: she puts 1 through 141 in order from top to bottom into column 1, then 142 through 282 into column 2 in order from top to bottom, and continues similarly through column 91. How many squares get two copies of the same number?

\textbf{(A)} 7 \qquad \textbf{(B)} 10 \qquad \textbf{(C)} 11 \qquad \textbf{(D)} 12 \qquad \textbf{(E)} 19

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.