Find all values of p that give a unicity distance larger

Question

We wish to encrypt a memoryless source with alphabet M = {0, 1, 2} and P(M = 0) = 1/2, P(M = 1) = p, P(M = 2) = 1/2 - p, 0 ≤ p ≤ 1/2.

Let the key K = (K₀, K₁, K₂), be chosen uniformaly from the get of binary 3-tuptfs. A sequence of messages M₁, M₂...M_n is encrypted to a sequence of ciphertext C1, C2, .....Cn by,

C_i = M_i + K_{imod 3}(mod 3). ∀i., 1 ≤ i ≤ n.

a) Find all values of p that give a unicity distance larger than 20.

b) Let p = 0. Propose a new cipher for this source that has an infinity inticity distance.