You're standing in front of a square mirror that's 300 mm on a side. There's a tiled wall behind you in which the tiles are squares 150 mm on a side. When you look in the mirror, you see exactly 25 of these tiles--or rather you would, if your body didn't get in the way of some of them.

Without being told the width of the room, identify what fraction of the way from the mirror to the tiled wall that you are located.

(In reply to We are not done yet! by Hugo)

Suppose you are not standing before the center of mirror,then just adjust your position so that you again see only 25 tiles as you know you can do that.But before adjusting your self to another position mark your initial position from where you were able to see 25 tiles.Mark your new position,now you are on any one side of the first mark either left or right try the same adjustment on other side of initial mark.Now you have marks of 3 positions,& most amazing thing which you may observe all pts lie in a straight line.

I wish i should have shown it diagramatically,you keep on adjusting your self to new position but all would fall on a straight line.So it does't matter if you are not standing at the centre of mirror the ratio will be 2/3,imagine it as a line dividing the distance between wall and mirror in ratio of 2/3.

But remmember you won't be able to see 25 tiles from all the positions on this line only few points are allowed,from the rest you will see some tiles completly and some cut partially.

Posted by Nishant on 2007-04-14 06:15:04