By clue 1, the numbers in the bottom row sum to 28, so that the possible numbers in the bottom row are 9-8-7-4 and 9-8-6-5.
By clue 4, the rightmost numbers in the four rows total 11. Therefore, 9 cannot be rightmost in row 4 since there is no combination of numbers with 9 that add to 11.
If 8 were in the bottom right location, then the other rightmost numbers would be 0, 1, and 2 with one of them at the apex--not possible given clue 6.
If 7 were in the bottom right location, then the other rightmost numbers would be 0, 1, and 3 with one of them at the apex--again not possible given clue 6.
If 6 were in the bottom right location, then the other rightmost numbers would be 0, 2, and 3 with one of them at the apex--again not possible given clue 6--or 0, 1, and 4, with the 4 at the apex (clue 6)-- but 0 would also have to be leftmost in row 2 (clue 6).
If 5 were in the bottom right location, then the other rightmost numbers would be 0, 2, and 4 with the 4 at the apex (clue 6)--but 0 would also have to be leftmost in row 2 (6)--or 1,2, and 3 and also impossible given clue 4.
So, 4 is the rightmost number in row 4 with 9, 8, and 7 being the other bottom row numbers.
Given clue 4, the other rightmost numbers are 0, 2, and 5 or 0, 1, and 6.
Trying the first possibility, 5 would be at the apex and 1 leftmost in row 2 (clue 6).
By clue 7, the four leftmost numbers in the rows sum to 20. Given the 9, 8, and 7 in row 4, the only arrangement possible is 8 leftmost in row 4 and 6 then leftmost in row 3; however, none of the remaining numbers in row 3 can be bigger than 6, contradicting clue 2. So, the rightmost numbers must be 0, 1, and 6, with 6 at the apex and 2 leftmost in row 2 (clue 6).
By clue 7, the four leftmost numbers in the rows sum to 20. Given the 9, 8, and 7 in row 4, the only arrangements possible are 7 leftmost in row 4 with 5 leftmost in row 3 or 9 leftmost in row 4 with 3 leftmost in row 3.
If 5 were leftmost in row 3, however, clue 2 could not work. So, 3 is leftmost in row 3 and 9 is leftmost in row 4. By clue 2, 5 is in the middle of row 3. By clue 3, 7 is next to 9 in row 4, with 8 to the right of 7. Finally, 0 is rightmost in row 2 and 1 is rightmost in row 3 (clue 5).
The final arrangement of the apartment numbers is as shown below:
Since apartment numbered 6 is on the top floor, it has the largest area.
Answer: 6