MathDB

For any integer

n\geq 2

, let

N(n)

be the maxima number of triples

(a_i, b_i, c_i)

i=1, \ldots, N(n)

, consisting of nonnegative integers

a_i

b_i

and

c_i

such that the following two conditions are satisfied: [*]

a_i+b_i+c_i=n

for all

i=1, \ldots, N(n)

, [*] If

i\neq j

then

a_i\neq a_j

b_i\neq b_j

and

c_i\neq c_j

Determine

N(n)

for all

n\geq 2

.
Proposed by Dan Schwarz, Romania

Problem Statement