The digits 1 to 9 are arranged in three rows in such a way that each row contains three digits, and the number formed in the second row is twice the number formed in the first row; and the number formed in the third row is thrice the number formed in the first row. Repetition of digits is not allowed. If only three of the four digits 2, 3, 7 and 9 are allowed to use in the first row, how many such combinations are possible to be arranged in the three rows?

• Let the number in the first row be $N$. The digits of $N$ must be chosen from the set {2, 3, 7, 9}, excluding exactly one digit, so $N$ is a 3-digit number formed by three of these four digits.

• The second row is $2N$ and the third row is $3N$. The union of the digits in $N$, $2N$, and $3N$ must be exactly the set {1, 2, 3, 4, 5, 6, 7, 8, 9} with no repetitions.

• We test the four possible values for $N$ by excluding one digit from {2, 3, 7, 9}:

1. Exclude 2: Digits {3, 7, 9}. Possible $N$ values: 379, 397, 739, 793, 937, 973. None of these produce valid $2N$ and $3N$ with distinct digits covering 1-9.

2. Exclude 3: Digits {2, 7, 9}. Possible $N$ values: 279, 297, 729, 792, 927, 972. Check $N=279$: $2N=558$ (repeat 5, invalid). Check $N=297$: $2N=594$ (repeat 9, invalid). Check $N=729$: $2N=1458$ (4 digits, invalid). Check $N=792$: $2N=1584$ (4 digits, invalid). Check $N=927$: $2N=1854$ (4 digits, invalid). Check $N=972$: $2N=1944$ (repeat 4, invalid).

3. Exclude 7: Digits {2, 3, 9}. Possible $N$ values: 239, 293, 329, 392, 923, 932. Check $N=239$: $2N=478$, $3N=717$ (repeat 7, invalid). Check $N=293$: $2N=586$, $3N=879$ (repeat 8,9? No, digits are 2,9,3,5,8,6,8,7,9 -> repeat 8 and 9). Check $N=329$: $2N=658$, $3N=987$. Digits: {3,2,9}, {6,5,8}, {9,8,7}. Repeat 9 and 8. Invalid. Check $N=392$: $2N=784$, $3N=1176$ (4 digits, invalid). Check $N=923$: $2N=1846$ (4 digits, invalid). Check $N=932$: $2N=1864$ (4 digits, invalid).

4. Exclude 9: Digits {2, 3, 7}. Possible $N$ values: 237, 273, 327, 372, 723, 732. Check $N=237$: $2N=474$ (repeat 4, invalid). Check $N=273$: $2N=546$, $3N=819$. Digits: {2,7,3}, {5,4,6}, {8,1,9}. Union: {1,2,3,4,5,6,7,8,9}. All distinct. Valid.

Check $N=327$: $2N=654$, $3N=981$. Digits: {3,2,7}, {6,5,4}, {9,8,1}. Union: {1,2,3,4,5,6,7,8,9}. All distinct. Valid.

Check $N=372$: $2N=744$ (repeat 4, invalid). Check $N=723$: $2N=1446$ (repeat 4, invalid). Check $N=732$: $2N=1464$ (repeat 4, invalid).

• Only two combinations ($N=273$ and $N=327$) satisfy all conditions.