| 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 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
(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:
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