IMO Shortlist 2007 problem C1
Dodao/la:
arhiva2. travnja 2012. Let
![n > 1](/media/m/c/8/9/c8999d29e042cf52e485c7a7b7301b0a.png)
be an integer. Find all sequences
![a_1, a_2, \ldots a_{n^2 + n}](/media/m/a/0/0/a00be444444d6e90e54ba22fe21c087f.png)
satisfying the following conditions:
![\text{ (a) } a_i \in \left\{0,1\right\}](/media/m/d/9/9/d9998a660a88fa6ea89bdb6c2e6decf6.png)
for all
![\text{ (b) } a_{i + 1} + a_{i + 2} + \ldots + a_{i + n} < a_{i + n + 1} + a_{i + n + 2} + \ldots + a_{i + 2n}](/media/m/3/e/c/3eceec10f2ce58cc5160933e5fad4648.png)
for all
![0 \leq i \leq n^2 - n](/media/m/7/b/7/7b7d56a312ac0b280d5befe1bef72c23.png)
Author: unknown author, Serbia
%V0
Let $n > 1$ be an integer. Find all sequences $a_1, a_2, \ldots a_{n^2 + n}$ satisfying the following conditions:
$\text{ (a) } a_i \in \left\{0,1\right\}$ for all $1 \leq i \leq n^2 + n;$
$\text{ (b) } a_{i + 1} + a_{i + 2} + \ldots + a_{i + n} < a_{i + n + 1} + a_{i + n + 2} + \ldots + a_{i + 2n}$ for all $0 \leq i \leq n^2 - n$
Author: unknown author, Serbia
Izvor: Međunarodna matematička olimpijada, shortlist 2007