MathDB

A set

S

consists of

k

sequences of

0,1,2

of length

n

. For any two sequences

(a_i),(b_i)\in S

we can construct a new sequence

(c_i)

such that

c_i=\left\lfloor\frac{a_i+b_i+1}2\right\rfloor

and include it in

S

. Assume that after performing finitely many such operations we obtain all the

3n

sequences of

0,1,2

of length

n

. Find the least possible value of

k

Problem Statement