AMC 10 2025 Part B 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 left to right in row 1, 92 through 182 in row 2, and so on. Vera fills the grid vertically: she puts 1 through 141 top to bottom into column 1, then 142 through 282 into column 2, and so on. How many squares get two copies of the same number?

Answer Choices:

A. 7

B. 10

C. 11

D. 12

E. 19