2024 AIME II Problem 3

Find the number of ways to place a digit in each cell of a 2 \times 3 grid so that the sum of the two numbers formed by reading left to right is 999, and the sum of the three numbers formed by reading top to bottom is 99. The grid below is an example of such an arrangement because 8 + 991 = 999 and 9 + 9 + 81 = 99.

Leading zeroes must be inputted, so if your answer is 34, then input 034

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