MathDB

Let

\mathcal{A}_n

be the set of

n

-tuples

x = (x_1, ..., x_n)

with

x_i \in \{0, 1, 2\}

. A triple

x, y, z

of distinct elements of

\mathcal{A}_n

is called good if there is some

i

such that

\{x_i, y_i, z_i\} = \{0, 1, 2\}

. A subset

A

\mathcal{A}_n

is called good if every three distinct elements of

A

form a good triple. Prove that every good subset of

\mathcal{A}_n

has at most

2(\frac{3}{2})^n

elements.

C1