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Points in a rectangle

Posted on: November 24th, 2013 by

If you choose 6 points inside a rectangle of dimensions 3cm x 4cm, show that the distance between some two of these 6 points is less than \sqrt{5}.

- via Math puzzles

2 Responses to Points in a rectangle

  1. Sid Hollander had this to say about that:

    Based upon given that the 6 points must be INSIDE the rectangle none can be ON the rectangle.

    If the horizontal measurement is 4in draw a vertical line at 2in and horizontal segments at 1 and 2..thus forming 6 rectangles each of 1 by 2. The longest distance in any one of these is sqrt of 5. Clearly any 2 points in one of these rectangles is less than sqrt 5. This means that each point must be in each rectangle. Since each diagonal must contain a point on the original 3 by 4 clearly the there must be least 2 points < sqrt 5.

  2. Lizard had this to say about that:

    I don't get the last step.

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