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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 6 of 10 |
I got 2/3 just like nikki, Fletch, and Hugo.

I drew a trapezoid to represent the room viewed from above:
        A                   B
         ************        Top is 300
       *                      *
     *                          *
   *              I               *
 *                                  *
***********************  Bottom is 750
C                                     D

Since the distance from mirror to back wall doesn't matter, I can make it anything I want, so I choose to make it whatever it needs to be so the angles are all 45 degrees (or 135 degrees), just to make the math easy.

So the altitude of the trapezoid is (750-300)/2 = 225
Reflect lines of equal incidence and reflection from CA to AI, and then from DB to BI.   Now ABI is a 45 degree right triangle, so the distance from the center of AB to I is 150.
So the answer is 150/225 = 2/3.  

        A                   B
         ************        
       *  *              *   *
     *       *        *        *
   *              I               *
 *                                  *
*********************** 
C                                     D

No matter what the distance from the mirror to the back wall, the ratio will be the same, just like taking the above sketch and warping the aspect ratio.

  Posted by Larry on 2005-01-13 20:56:22
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