# Deduce Linear Order from Relations

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A list of objects is given. The objects can be figures, letters or digits. Write down the arrangement of the objects to appear in the row of red squares so that the given statements are true, then check your solution. The statement can involve binary relations "left of," "right of" and "besides" and ternary relations like "A is between B and C" and "1 is equally distant from 2 and 3."

Contributed by: Izidor Hafner (July 2018)

Open content licensed under CC BY-NC-SA

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## Details

If A is between B and C, A is not necessarily adjacent to B or C.

M. Piery has shown that a ternary relation, that of a point being equally distant from two other points, can be used as the only primitive notion of Euclidean geometry of two or more dimensions [1, p. 68].

Reference

[1] R. M. Robinson, "Binary Relations as Primitive Notions in Elementary Geometry: The Axiomatic Method with Special Reference to Geometry and Physics," in *Proceedings of an International Symposium Held at the University of California, Berkeley, December 26, 1957–January 4, 1958*, Amsterdam: North-Holland Publishing Company, 1959 pp. 68–85. doi:10.1017/S0022481200092690.

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