 Home Contact Help Log In not logged in Number Pyramid 14    Even Moses would like working on this Number Pyramid.
 November 21, 2008 By clue 2, the middle number in row 3 minus the rightmost number in row 3 equals 4, so that the highest number possible in the rightmost position of row 3 is 5. By clue 3, the four numbers in row four sum to 8, so that the highest number in the rightmost position of row 4 is also 5. By clue 1, the number at the apex of the pyramid minus the leftmost number in row 4 equals 7, so that the possible numbers at the apex and leftmost in the bottom row are 7-0, 8-1, or 9-2, respectively. If the numbers were 7 at the apex and 0 leftmost in row 4, since the apex and rightmost numbers in rows 2, 3, and 4 sum to 25 (clue 5), the rightmost numbers in rows 2, 3, and 4 would sum to 18. This would give four possible number combinations for the rightmost numbers in rows 2, 3, and 4: 9-8-1, 9-6-3, 9-5-4, and 8-6-4. Given the clues 2 and 3 caps on the rightmost numbers in rows 3 and 4, combinations 9-8-1, 9-6-3, and 8-6-4 would be impossible. Trying 9-5-4, by clues 2 and 3, 9 would be rightmost in row 2. Then 5 could not be rightmost in row 3 (2), so 4 would be, with 5 rightmost in row 4. The middle number in row 3 would be 8 (2). However, there is no way for clue 4 to work given this arrangement. So, 7-0 aren't at the apex and leftmost in row 4. If the numbers were 8 at the apex and 1 leftmost in row 4, since the apex and rightmost numbers in rows 2, 3, and 4 sum to 25 (5), the rightmost numbers in rows 2, 3, and 4 would sum to 17. This would give four possible number combinations for the rightmost numbers in rows 2, 3, and 4: 9-7-1, 9-6-2, 9-5-3, and 7-6-4. Given the clues 2 and 3 caps on the rightmost numbers in rows 3 and 4 being at most 5, any combination with 9 in it would put 9 rightmost in row 2 and 8 then to its left (4)--impossible since 8 would be at the apex. The clues 2 and 3 caps of 5 on the rightmost numbers in rows 3 and 4 would also eliminate 7-6-4 as a possibility. So, 8-1 aren't at the apex and leftmost in row 4. 9 is at the apex and 2 leftmost in row 4 of Number Pyramid 14. Since the apex and rightmost numbers in rows 2, 3, and 4 sum to 25 (5), the rightmost numbers in rows 2, 3, and 4 would sum to 16. This would give five possible number combinations for the rightmost numbers in rows 2, 3, and 4: 8-7-1, 8-6-2, 8-5-3, 7-6-3, and 7-5-4. Given the clues 2 and 3 caps on the rightmost numbers in rows 3 and 4 being at most 5, combinations 8-7-1, 8-6-2, and 7-6-3 are impossible. Trying 8-5-3, by clues 2 and 3, 8 would be rightmost in row 2 with 7 to its left (4). Since 9 is at the apex, by clue 2, 5 couldn't be rightmost in row 3 and would be rightmost in row 4, with 3 then rightmost in row 3. However, the middle number in row 3 would be 7 (2)--no. So, the rightmost numbers are 7-5-4 in some order. By clues 2 and 3, 7 is rightmost in row 2--with 6 to its left (4). By clue 2, 5 is rightmost in row 4 rather than row 3, with 4 rightmost in row 3. 8 is in the middle of row 3 (2). Since row 4 sums to 8, 0 and 1 complete it--by clue 6, 0 is second and 1 third from the left in row 4. Finally, 3 is the leftmost number in row 3. In sum, Number Pyramid 14 is filled as follows:     9    6 7   3 8 4  2 0 1 5 Copyright © 2002-2021 Infinitas LLC. All rights reserved. Contact | Help | Privacy Policy 