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Odd numbers (Posted on 2014-04-20) Difficulty: 3 of 5
Place 4 points in a plane so, that the 6 point-to-point distances will be integers and at least 5 of them will be odd.

No Solution Yet Submitted by Ady TZIDON    
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Solution Solution Comment 1 of 1

The law of cosines helps.

The following triangles have integer sides where the angle in degrees is the angle between the first two sides:

3, 8, 7 (60 degrees)
5, 8, 7 (60 degrees)
3, 5, 7 (120 degrees).

Consider the following layout:

              A

B                        C

             D

Where AB is 5; AC is 3; BC is 7; BD is 7; CD is 7; AD is 8.

Angle BAD is 60 degrees
Angle DAC is 60 degrees
Angle BAC is 120 degrees
Triangle BDC is equilateral, all sides being 7

Edited on April 20, 2014, 7:44 pm
  Posted by Larry on 2014-04-20 19:42:36

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