By clue 1, the four numbers in the fourth row of Number Pyramid 8 sum
to 12; while by clue 4, the top number plus the two numbers in the second
row of Number Pyramid 8 equal 17a total of 29. Since the nine
numbers in the pyramid add up to 45, the three numbers in the third row must
total 16. By clue 2, in row 3, the leftmost number minus the rightmost
number equals 7. There are thus three possible arrangements of row 3
lefttoright: 952, 871, and 790. Since the 6 isn't in row 4 (1),
it must be in the top two rows of the pyramid. Trying third row sequence
952, since the top three numbers in the pyramid sum to 17 and 6 is one
of them, the other two numbers would have to be 7 and 4 or 8 and 3. If
they were 7 and 4, by clue 3, either 7 or 6 would be at the apex and 1 or 0
then rightmost in row 4. If 7 were at the apex and 1 rightmost in row 4,
by clue 5, the rightmost number in row 2 would be 5no. If 6 were at the
apex and 0 rightmost in row 4, by clue 5, the rightmost number in row 2
would be the 7, with 4 then leftmost in row 2. The other three numbers in
row 4 would then be 8, 3, and 1 in some orderbut there is no way for clue
6 to work. If the numbers with 6 at the top of the pyramid were 8 and 3, by
clue 3, 6 would be at the apex and 0 then rightmost in row 4. However, 7
would be the rightmost number in row 2 (clue 5)no. So, 952 is not the
sequence across row 3 of Number Pyramid 8. Trying third row sequence
790, since the top three numbers in the pyramid sum to 17 and 6 is one of
them, the other two numbers would have to be 8 and 3. By clue 3, the 8
would be at the pyramid apex and 2 then rightmost in row 4. By clue 5, then,
the rightmost number in row 2 would be 5no. So, 790 is not the sequence
across row 3 of Number Pyramid 8; 871 is. Since the top three
numbers in the pyramid sum to 17 and 6 is one of them, the other two numbers
would have to be 9 and 2. By clue 3, either the 6 or 9 is at the apex of
the pyramid with either 0 or 3 then rightmost in row 4. If 6 were at the
apex and 0 rightmost, by clue 5 the rightmost number in row 2 would be 8no.
So, 9 is at the apex of the pyramid and 3 rightmost in row 4. By clue 5,
2 is rightmost in row 2 and 6 then leftmost in row 2. The other three
numbers in row 4 must be 0, 4, and 5 in some order. By clue 6, the leftmost
number is 5 and the number next to it 4, with the 0 the third letter across
row 4. In sum, Number Pyramid 8 is filled as follows:


