olymmath

TSTST 2011 Problem 1

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Find all real-valued functions ff defined on pairs of real numbers, having the following property: for all real numbers a,b,ca, b, c, the median of f(a,b),f(b,c),f(c,a)f(a, b), f(b, c), f(c, a) equals the median of a,b,ca, b, c. (The median of three real numbers, not necessarily distinct, is the number that is in the middle when the three numbers are arranged in nondecreasing order.)

Dataset text NuminaMath olympiads. Quoted with source.

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f(x, y) \equiv x \text{ or } f(x, y) \equiv y

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