There are some children on a school ground, a square has been drawn and all children are standing on a squares four lines, they are standing with same distance, four children are standing on a four corners. No 16 Is exactly opposite of No 6. How many children are there?
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Assuming there are x children in every side of the square, thus a total of 4x -4 children will be there(not counting corner child twice).
Now we know there are atleast 16 children, thus 4x-4 >= 16. x >= 5
Lets assume first child is sitting on bottom left corner, than assume three cases
Case 1: x = 5
then 6th child will be standing on second position in second line of square, thus the exactly opposite child will be sitting on x + x-2 + x + x-1 = 4x-3th position, i.e. 17th position.
Which is not the case as per the question, thus x can’t be 5
Case 2: x = 6
then 6th child is sitting on the corner(point B), thus exactly opposite child is on x + x-2 + x= 3x-2th position, i.e. 16th.
Thus it satisfies all conditions of the question.
Thus there are a total of 4x-4, i.e. 20 children in this case.
Case 3: x > 6
then 6th child is standing somewhere in the bottom line (point A), as per this exactly opposite child will be standing at position x + x-2 + x -6 = 3x – 8
for 3x-8 = 16 => x = 24/3 = 8
Thus there are a total of 4x-4 = 28 children in this case.