Intransitive urns

Question

N balls with numbers 1,2,3...N are filled arbitrarily into 3 urns A,B and C - but no urn may remain empty. We write P(A,B) for the probability that a ball chosen randomly from urn A shows a higher number than a ball chosen randomly from urn B. We call the tree urns intransitive if P(A,B)>1/2, P(B,C)>1/2 and P(C,A)>1/2.

1. Give the smallest possible N and the corresponding contents of the urns such that the three urns are intransitive.
2. Give the smallest possible N and the corresponding contents of the urns such that additionally P(A,B)=P(B,C)=P(C,A).

Answer 1

N=7 (1,5,6,),(4),(2,3,7)

N=9 (2,6,7),(1,5,9),(3,4,8) P=5/9

or

(1,6,8),(3,5,7),(2,4,9)