MEMO 2012 ekipno problem 3
Kvaliteta:
Avg: 0,0Težina:
Avg: 0,0 Let
be a positive integer. Consider words of length
composed of letters from the set
. Let
be the number of such words containing an even number (possibly 0) of blocks
and an even number (possibly 0) blocks of
. Similarly let
the number of such words containing an odd number of blocks
and an odd number of blocks
. Prove that
.
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![\{ M, E, O \}](/media/m/8/5/3/853d6ecb665bf9929d86a49596ce78da.png)
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
![ME](/media/m/0/9/f/09fe7f54e93fe547123cecfc182bc6e2.png)
![MO](/media/m/4/b/3/4b3f6143964c0f904266b94364775916.png)
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
![ME](/media/m/0/9/f/09fe7f54e93fe547123cecfc182bc6e2.png)
![MO](/media/m/4/b/3/4b3f6143964c0f904266b94364775916.png)
![a>b](/media/m/9/3/e/93ec187b4eea9a155615a5025c8701f3.png)
Izvor: Srednjoeuropska matematička olimpijada 2012, ekipno natjecanje, problem 3