IBM Ponder This #097 · May 2006

Puzzle for May 2006.

This month's puzzle concerns configurations of 4 distinct points in the plane.  Suppose we know the 6 distances between pairs of points only take on two values.  We ask for a list of the distinct possible configurations.  For each configuration give the number of long distances and the number of short distances (which must sum to 6) and the ratio of the long distance to the short distance.

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The first 100 people who answer all parts correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.

Solution

Best opened after a real attempt

To be added.