| By clue 1, the two numbers in the 2nd row of Number Pyramid 11 sum
to 14, so that the possible left-to-right combinations are 9-5, 8-6, 6-8,
and 5-9. Since the leftmost numbers in the four rows sum to 11 (clue 4),
9 can't be leftmost in row 2 because the other three numbers would sum
to 2. If 8 were the leftmost number in row 2, the other three leftmost
numbers would add to 3 (4) and would have to be 0, 1, and 2, in some order.
However, 1 and 2 would then be in different rows of the pyramid--no (6).
If 5-9 were the left-right pair in row 2, the other three leftmost numbers
would sum to 6 (4) and would have to be 1, 2, and 3 in some order or
0, 2, and 4 in some order. The numbers can't be 1, 2, and 3 in some order,
since 1 and 2 are in the same row (6). If the numbers were 0, 2, and 4,
since 0 isn't at the apex of the pyramid (2) and since 2 is in the same row
as 1 (6) and thus couldn't be at the apex, 4 would be at the apex of the
pyramid. However, the rightmost number in row 4 would be 5 (7)--impossible,
since 5 would be the leftmost number in row 2. Therefore, 6 and then 8 are
in row 2 of Number Pyramid 11. The other three leftmost letters
then add to 5 (4) and must be 0, 1, and 4 in some order or 0, 2, and 3 in
some order. If the numbers were 0, 2, and 3, since 0 isn't at the apex of
the pyramid (2) and since 2 is in the same row as 1 (6) and thus couldn't
be at the apex, 3 would be at the apex of the pyramid. If 2 were the
leftmost number in row 3 and 0 leftmost in row 4, 1 would be next to 0
(3)--a contradiction with 6. If 0 were the leftmost number in row 3 and
2 leftmost in row 4, 3 would be next to 2--impossible, since 3 would be
at the pyramid apex. So, the other three leftmost letters are 0, 1, and 4
in some order. Since 0 isn't at the apex of the pyramid (2) and since 1
is in the same row as 2 (6) and thus couldn't be at the apex, 4 is at the
apex of the pyramid. If 1 were the leftmost number in row 3 and 0 leftmost
in row 4, 1 would also be next to 0 (3). 0 is the leftmost number in row 3
and 1 leftmost in row 4. By clue 7, the rightmost number in row 4 is 5.
2 is to 1's immediate right in row 4 (3). With the remaining three numbers
being 3, 7, and 9, the only way for clue 5 to work is for 7 to be in the
middle of row 3 with 9 to its right. 3 is in row 4 between 2 and 5.
In sum, Number Pyramid 11 is filled as follows:
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