By clue 3, the three numbers in the third row of Number Pyramid 9 sum
to 24; they must be 7, 8, and 9 in some order. By clue 4, the four leftmost
numbers also add up to 24. If in row 3 either 7 or 8 were the leftmost
number, the most the four leftmost numbers in each row could sum to would
be 22 (7, 6, 5, 4) or 23 (8, 6, 5, 4). So, 9 is leftmost in row 3, with 4,
5, and 6 then leftmost in the other rows in some order. By clue 1, the
number on top the pyramid minus the sum of the two numbers in the second row
equals 1. 4 cannot be at the apex of the pyramid, since row 2 would have
at least a 5 or 6 in it. If 5 were atop the pyramid, then row 2 would have
4 and 0 across it (clue 1), with 6 leftmost in row 4. However, given the
remaining numbers of 1, 2, and 3 in row 4, there would be no way for clue 5 to
work. Therefore, the number atop the pyramid is 6. By clue 1, row 2 has
either 5, 0 or 4, 1 across it. If 5, 0 were in row 2 with 4 leftmost in
row 4, however, given the remaining numbers of 1, 2, and 3 in row 4, there
would be no way for clue 5 to work. So, row 2 has 4, 1 across it, with 5
leftmost in row 4. Given the remaining numbers in row 4 of 0, 2, and 3 and
given clue 5, the rightmost number in row 4 is 3 and the number second from
the left is 0. 2 is between them to complete the row. Finally, by clue 2,
8 is in the middle and 7 rightmost in row 3. In sum, Number Pyramid 9
is filled as follows:


