MathDB
2004 General, part 1 #8

Source:

March 8, 2024
combinatorics

Problem Statement

You have a 10×1010\times 10 grid of squares. You write a number in each square as follows: you write 11, 22, 33 ,... ... ,1010 from left to right across the top row, then 1111, 1212, ......, 2020 across the second row, and so on, ending with a 100100 in the bottom right square. You then write a second number in each square, writing 11, 22, 33 ,... ... ,1010 in the first column (from top to bottom), then 1111, 1212, ......, 2020 in the second column, and so forth. When this process is finished, how many squares will have the property that their two numbers sum to 101101?
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