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Three Lock Box (Posted on 2010-07-19) Difficulty: 3 of 5
You are asked to help design a Three Lock Box. Your job is to decide the locations of the three locks. The door is a unit square. To operate properly, each lock must be the same distance from the nearest door edge and also that same distance from each of the other two locks.

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Solution Solution | Comment 2 of 4 |

Each lock, respective to each other, act as vertices of an equilateral triangle. By placing a base of the triangle parallel to one edge of the square door, the two vertices of that triangle to the other two sides of the square door would need to be the same distance. Thus, the length of the side maybe be 1/3.

The height of the equilateral-triangular lock box, would then be 
SQRT((1/3)^2 - (1/2*1/3)^2) or 1/2·SQRT(3) or approximately 0.288675, which is less than the limit of 1/3.

Edited on July 20, 2010, 8:54 am
  Posted by Dej Mar on 2010-07-19 18:37:31

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