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Mirror in the bathroom. (Posted on 2005-01-13) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Juggler    
Rating: 4.0000 (2 votes)

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Solution Solution | Comment 1 of 10
I suppose that you are standing in the center of the mirror.
The surface you see behind you is a square with sides 150 x SQRT(25) or 750 mm side. 
The reflection angle of the light in the mirror is the same as the entrance angle (I suppose it is a flat mirror).  Now draw a triangle from yourself to the edges of the mirror and from these points draw a line to the wall behind you.
Mirror this triangle around the mirror (This indeed sounds strange), this way you would be behind the mirror, on the top of an equilateral triangle.  The distance you are from the mirror is 300/750 or 40 % of the distance between the mirror and the wall 
  Posted by Hugo on 2005-01-13 13:38:21
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