Question

Write the set of all positive integers in triangular array as 1 3 6 10 15 2 5 9 14 4 8 13 7 12 11 find the row number and column number where 20096 occurs. For example 8 appears in the third row and second column.

Answer 1

Answer:

Step-by-step explanation:

OK, let's look how would I get it.

First, we can determine the id of the anti-diagonal, denoted by n at which a value X would be by using the following trick:

The number of all elements to left of this anti-diagonal n is a sum of arithmetic series, hence, Sn=n(n−1)/2.

We know that X belongs to anti-diagonal n and Sn>Sn−1. Hence, we solve the equation Sn=X to get n as follows:

n(n−1)/2=X→n=⌈8X−1−−−−−−√−12⌉

For this anti diagonal elements, i+j=n+1 and the first element (at i=n and j=1) is A=1+n(n−1)/2.

Let d=X−A, then the position of X is: i=n−d and j=1+d.

Hope it helps you....

Answer 2

5, 12, 13 9, 40, 41

5,12,13 Triangle 9,40,41 Triangle

52 + 122 = 132 92 + 402 = 412

25 + 144 = 169 (try it yourself)