By clue 5, the sum of the numbers in rows 3 and 4 is 40, leaving a total of
5 for the three numbers in the top two rows of the Pyramid. 5 can be made
either by 014 or 023; however, since the difference between the two
numbers in row 2 is 2 (clue 3), only 023 will work, with the arrangement
in row 2 either 02 or 20 leftandright and 3 at the apex of the Pyramid.
By clue 6, the four leftmost numbers of each row sum to 9. Only three number
combinations from 09 add to 9: 0126, 0234, and 0135. The first
arrangement fails since 3 is at the top, while the second arrangement fails
because one of 0 and 2 must be rightmost in row 2. So, 0 is leftmost and 2
rightmost in row 2, with either 1 or 5 leftmost in row 3. However, 1 cannot
be the leftmost number, since by clue 5, the other two numbers in row 3 would
have to sum to an impossuble 19. So, 5 is the leftmost number in row 3 and
1 the leftmost in row 4, with 4 to its right (4). The remaining two numbers
in both row 3 and 4 sum to 15 (5). If the numbers in row 4 were 6 and 9,
there would be no way for 7 or 8 to work as the middle digit in row 4 (1).
So, the remaining two numbers in row 4 are 7 and 8 leftandright (2), while
6 and then 9 complete row 4 (1). In sum, Number Pyramid 4 looks like
this:


