Crazy Inequalities

Algebra Level 2

Given three numbers such that 0<a<b<c<1 0 < a < b < c < 1, define

A=aabbcc,B=aabccb,C=abbcca. A = a^{a}b^{b}c^{c}, \quad B = a^{a}b^{c}c^{b} , \quad C = a^{b}b^{c}c^{a}.

How do the values of A,B,CA, B, C compare to each other?

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