## Two Scarecrows

1. Tom, Dick and Harry are sitting in a cornfield, in which there are two scarecrows. One of the scarecrows (S1) lies mid-way between Dick and Harry, while the other one (S2) lies mid-way between Tom and Harry. Tom is 8 yards from S1, while Dick is an integral number of yards from each of Tom, Harry, S1 and S2. Assume that no straight line can go through all the 3 guys. What are the possible distances of Tom, Harry and S2 from Dick?
2. If Tom is also an integral number of yards from Harry, can you find a solution?
3. If no answer exists for part 2, can you find a distance between Tom and S1, such that all distances are integral?

Source: Created by reader Sudipta Das.

Denis Borris suggested an extension to this puzzle:
Tom, Dick and Harry are sitting in a cornfield, in which there are three scarecrows. One of the scarecrows (S1) lies mid-way between Dick and Harry, another (S2) lies mid-way between Tom and Harry, and the 3rd one (S3) lies mid-way between Tom and Dick. The distance between any of the 3 guys is even. The distance between any scarecrow and any guy is also even.
DistanceTom:Dick > distanceTom:Harry > distanceDick:Harry.
Distance Dick:Harry is at minimum. Find the above 3 distances.
Solution
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