The pyramid of integers above is constructed in such a way that each "father" has exactly 3 "children":
1>2,3,4
2>5,6,7
3>8,9,10
4>11,12,13
5>14,15,16
6>17,18,19
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.
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What number is the father of 2017?
n is the father of 3n-1,3n,3n+1
so, divide 2017 by 3 and check the remainder...
Thanks
To find the father of 2017, we need to determine the pattern in the pyramid structure.
Looking at the pyramid, we can observe that each row follows an arithmetic sequence. The first row starts with 1 and increments by 1 for each consecutive number. The second row starts with 2 and also increments by 1 for each successive number. This pattern continues for each row.
We can use this pattern to determine the row in which 2017 falls. By counting the number of numbers in each row, we can find the cumulative sum until the sum exceeds 2017.
Row 1: 1 (1 number)
Row 2: 2, 3 (2 numbers)
Row 3: 4, 5, 6 (3 numbers)
Row 4: 7, 8, 9, 10 (4 numbers)
Row 5: 11, 12, 13, 14, 15 (5 numbers)
...
Continuing this counting, we find that the cumulative sum exceeds 2017 in Row 45. Therefore, 2017 belongs to Row 45.
To determine the father of 2017, we need to find the starting number (father) of Row 45. To calculate this, we can use the formula:
starting number of Row n = 1 + (n - 1) * (n - 2)
For Row 45:
father of 2017 = 1 + (45 - 1) * (45 - 2)
father of 2017 = 1 + 44 * 43
father of 2017 = 1913
Therefore, the father of 2017 is 1913.