We can only use three of the four digits—2, 3, 7, and 9—in the first row.

Since the third row is a three-digit number and is thrice the first row number, the maximum possible value for the first row is $987/3 = 329$. This constraint narrows down the possible values of the first row to:

237, 273, 239, 293, 279, 297, 327, and 329.

Now, let’s check each of these values by doubling and tripling them to see if they satisfy the conditions without any digit repetition.

$237 \times 2 = 474$ (digit repetition, so eliminate) $273 \times 2 = 546$, $273 \times 3 = 819$ (No digit repetition, so this is a valid combination) $239 \times 2 = 478$, $239 \times 3 = 717$ (digit repetition, so eliminate) $293 \times 2 = 586$, $293 \times 3 = 879$ (digit repetition, so eliminate) $279 \times 2 = 558$ (digit repetition, so eliminate) $297 \times 2 = 594$, $297 \times 3 = 891$ (digit repetition, so eliminate) $327 \times 2 = 654$, $327 \times 3 = 981$ (No digit repetition, so this is a valid combination) $329 \times 2 = 658$, $329 \times 3 = 987$ (digit repetition, so eliminate)

After checking all cases, only 273 and 327 satisfy the conditions without digit repetition.