Question

You have a Square table and it is filled with natural numbers in sequence. Two of them are given for your reference
3X3
1 2 3
4 5 6
7 8 9
4X4
1
2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
In the above quad sum of number at diagonal is 6+11 = 17
Now using above table do the following -
1. Select any quad of numbers (2X2)( as shown in pic ) and find out if there is any pattern you see in sum of diagonal elements
2. To get the answer you can make more such square table like 5X5 and 6X6 type.
3. Can you formulate an algebraic equation for above pattern for NXN type of a square table where N represent no of rows & columns?
4. Is there any pattern visible if you take difference between sum of diagonal element in a chosen quad?
5. Can you write an algebraic equation for it too?

Answer 1

any number add diagonally the sum of the digits is odd