By clue 1, the numbers in the bottom row of Number Pyramid 13 sum to
28, so that the possible numbers in the bottom row are 9874 and 9865.
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 apexnot
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
apexagain 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 apexagain not possible given clue 6or 0, 1, and 4, with
the 4 at the apex (clue 6)but 0 would also have to be leftmost in row 2
(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 (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
arrangment 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 (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 (5). In sum, Number Pyramid 13 is filled
as follows:


