IMO Shortlist 1973 problem 8
Dodao/la:
arhiva2. travnja 2012. Prove that there are exactly
![\binom{k}{[k/2]}](/media/m/4/b/2/4b281ba757f46151539d6a54187bf655.png)
arrays
![a_1, a_2, \ldots , a_{k+1}](/media/m/e/9/d/e9dc29e6ddec83bab4b9b95b990a41f3.png)
of nonnegative integers such that
![a_1 = 0](/media/m/d/1/5/d15bc56647a6ffa3a809adbfa07aa98b.png)
and
![|a_i-a_{i+1}| = 1](/media/m/f/a/c/facae649f3e49e6b84f4426bba951c9b.png)
for
%V0
Prove that there are exactly $\binom{k}{[k/2]}$ arrays $a_1, a_2, \ldots , a_{k+1}$ of nonnegative integers such that $a_1 = 0$ and $|a_i-a_{i+1}| = 1$ for $i = 1, 2, \ldots , k.$
Izvor: Međunarodna matematička olimpijada, shortlist 1973