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Question 1199519: In the following pattern, find the 9th number in the 19th row.
Pattern: https://ibb.co/N2bwG4C
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52908)   (Show Source):
You can put this solution on YOUR website! .
Kind of gibberish.
There is no 9-th number in NO ONE of presented rows.
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Hello, I got your comment.
All that I can say is that this piece of information, presented under the link,
is not an adequate description of the problem, as you keep it in your mind.
Re-write and re-post your problem to the forum, making the description adequate to the problem.
Answer by greenestamps(13215)  (Show Source):
You can put this solution on YOUR website!
Either the pattern is shown incorrectly, or the question is asked incorrectly.
With the pattern as shown in the given URL, the "rows" are DIAGONAL rows.
Perhaps it is easier to see what the question is if we write the array of numbers so that the rows are horizontal:
row #
1 1
2 2 3
3 6 5 4
4 7 8 9 10
5 15 14 13 12 11
6 16 17 18 19 20 21
7 28 27 26 25 24 23 22
... ...
... ...
It should be relatively easy to see the following from the pattern for row n:
If n is even, then the LAST number in the row in the n-th triangular number, and the numbers in the row are INCREASING left to right;
If n is odd, then the FIRST number in the row is the n-th triangular number, and the numbers in the row are DECREASING left to right.
We are to find the 9th number in the 19th row. The first number in the 19th row is the 19th triangular number, (19*20)/2 = 190, and in the 19th row the numbers are decreasing from left to right, so the 9th number in the 19th row is 190-8 = 182.
ANSWER: 182
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