IMO Shortlist 2001 problem C5
Dodao/la:
arhiva2. travnja 2012. Find all finite sequences
![(x_0, x_1, \ldots,x_n)](/media/m/c/9/7/c979058aba447c6bdac386f10ca8326f.png)
such that for every
![j](/media/m/7/9/e/79ebb10f98eb80d16b0c785d9d682a72.png)
,
![0 \leq j \leq n](/media/m/1/e/8/1e8edae6255dd4c793b6e5c2b0546653.png)
,
![x_j](/media/m/d/f/f/dff8463e86b3e9a0daede06c0d21dd63.png)
equals the number of times
![j](/media/m/7/9/e/79ebb10f98eb80d16b0c785d9d682a72.png)
appears in the sequence.
%V0
Find all finite sequences $(x_0, x_1, \ldots,x_n)$ such that for every $j$, $0 \leq j \leq n$, $x_j$ equals the number of times $j$ appears in the sequence.
Izvor: Međunarodna matematička olimpijada, shortlist 2001