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Number Pyramid 11
Tut-Tut if you can't solve today's Logic Puzzle.
February 11, 2008
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:

        4
       6 8
      0 7 9
     1 2 3 5

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