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 October 22, 2007 By clue 1, the three numbers in the top two rows of Number Pyramid 10 sum to 15; while by clue 4, the four numbers in row 4 sum to 26. From the introduction, the 10 numbers in the pyramid sum to 45; then the three numbers across row 3 of the pyramid must be 0, 1, and 3, in some order. Given this and that the three numbers in the top two rows of Number Pyramid 10 sum to 15 (clue 1), one of four possible sets of numbers fills the top two rows of the pyramid: 6, 5, 4; 7, 6, 2; 8, 5, 2; or 9, 4, 2. Trying 6, 5, 4, the numbers in row 4 would be 2, 7, 8, 9 in some order. By clue 5, 8 would be rightmost in row 4 and 3 leftmost in row 3. By clue 3, 5 would be rightmost in row 2 and 2 leftmost in row 4. However, there is no way for clue 2 to work given this arrangement. So, 6, 5, 4 isn't the set of numbers in rows 1 and 2. Trying 7, 6, 2, the numbers in row 4 would be 4, 5, 8, 9 in some order. By clue 6, 7 would be at the apex of the pyramid and 3 in the middle of row 3. However, there is no way for clue 5 to work given this arrangement. So, 7, 6, 2 isn't the set of numbers in rows 1 and 2. Trying 8, 5, 2, the numbers in row 4 would be 4, 6, 7, 9 in some order. By clue 5, the rightmost number in row 4 would be 6 and the leftmost number in row 3 would be 1. However, there is no way for clue 6 to work given this arrangement. So, 8, 5, 2 isn't the set of numbers in rows 1 and 2. The set of numbers in rows 1 and 2 is 9, 4, 2, with the four numbers in row 4 then 5, 6, 7, 8 in some order. By clue 6, 4 is at the apex of the pyramid with 0 in the middle of row 3. By clue 3, 9 is rightmost in row 2 and 6 leftmost in row 4. 2 is leftmost in row 2, by elimination. By clue 5, 8 is rightmost in row 4 and 3 leftmost in row 3. 1 is rightmost in row 3. Finally, 5 is second from the left in row 4 and 7 is third from the left (2). In sum, Number Pyramid 10 is filled as follows:     4    2 9   3 0 1  6 5 7 8  