MathDB

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

. [asy] unitsize(0.7cm); draw((0,0)--(3,0)); draw((0,1)--(3,1)); draw((0,2)--(3,2)); draw((0,0)--(0,2)); draw((1,0)--(1,2)); draw((2,0)--(2,2)); draw((3,0)--(3,2)); label("

9

", (0.5,0.5)); label("

9

", (1.5,0.5)); label("

1

", (2.5,0.5)); label("

0

", (0.5,1.5)); label("

0

", (1.5,1.5)); label("

8

", (2.5,1.5)); [/asy]

Problem Statement