Secvente de 0 si 1
Posted: Sat Jul 12, 2008 6:59 pm
Fie un intreg \( n > 1 \). Sa se gaseasca secventele de \( n^2 + n \) numere \( a_j \in \{ 0, 1\} \) satisfacand
\( a_{i + 1} + \cdots + a_{i + n} < a_{i + n + 1} + \cdots + a_{i + 2n} \), \( \forall i \in \overline{0, n^2 - n} \).
[ IMO Shortlist 2007, C1 ]
\( a_{i + 1} + \cdots + a_{i + n} < a_{i + n + 1} + \cdots + a_{i + 2n} \), \( \forall i \in \overline{0, n^2 - n} \).
[ IMO Shortlist 2007, C1 ]