Question 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 $9 + 9 + 81 = 99.$
