MathDB

Number-Theory related

Source: Iranian National Olympiad (3rd Round) 2006

September 11, 2006

modular arithmeticvectorfunctionlinear algebracombinatorics proposedcombinatorics

Problem Statement

Let

B

be a subset of

\mathbb{Z}_{3}^{n}

with the property that for every two distinct members

(a_{1},\ldots,a_{n})

and

(b_{1},\ldots,b_{n})

B

there exist

1\leq i\leq n

such that

a_{i}\equiv{b_{i}+1}\pmod{3}

. Prove that

|B| \leq 2^{n}