MathDB

Let

n

be an even number, and

S

be the set of all arrays of length

n

whose elements are from the set

\left\{0,1\right\}

. Prove that

S

can be partitioned into disjoint three-element subsets such that for each three arrays \left(a_i\right)_{i \equal{} 1}^n, \left(b_i\right)_{i \equal{} 1}^n, \left(c_i\right)_{i \equal{} 1}^n which belong to the same subset and for each

i\in\left\{1,2,...,n\right\}

, the number a_i \plus{} b_i \plus{} c_i is divisible by

2

Problem Statement