AMC 12A 2025 (Problem 18)

CombinatoricsHard

How many ordered triples

(x,y,z)

of different positive integers less than or equal to

8

satisfy

xy>z

xz>y

, and

yz>x

\text{(A)}\;36

\text{(B)}\;84

\text{(C)}\;186

\text{(D)}\;336

\text{(E)}\;486