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Number Pyramid 8
Is it Pharaoh to ask you to solve Number Pyramid 8?
April 2, 2007
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 17--a 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 left-to-right: 9-5-2, 8-7-1, and 7-9-0. Since the 6 isn't in row 4 (1), it must be in the top two rows of the pyramid. Trying third row sequence 9-5-2, 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 5--no. 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 order--but 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, 9-5-2 is not the sequence across row 3 of Number Pyramid 8. Trying third row sequence 7-9-0, 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 5--no. So, 7-9-0 is not the sequence across row 3 of Number Pyramid 8; 8-7-1 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 8--no. 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:

        9
       6 2
      8 7 1
     5 4 0 3

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