ISL 2007 C1

For discussing Olympiad Level Combinatorics problems
rah4927
Posts:110
Joined:Sat Feb 07, 2015 9:47 pm
ISL 2007 C1

Unread post by rah4927 » Tue Aug 16, 2016 12:53 am

Let $ n > 1$ be an integer. Find all sequences $ a_1, a_2, \ldots a_{n^2 + n}$ satisfying the following conditions:
\[ \text{ (a) } a_i \in \left\{0,1\right\} \text{ for all } 1 \leq i \leq n^2 + n;
\] \[ \text{ (b) } a_{i + 1} + a_{i + 2} + \ldots + a_{i + n} < a_{i + n + 1} + a_{i + n + 2} + \ldots + a_{i + 2n} \text{ for all } 0 \leq i \leq n^2 - n.
\]

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Zawadx
Posts:90
Joined:Fri Dec 28, 2012 8:35 pm

Re: ISL 2007 C1

Unread post by Zawadx » Tue Sep 20, 2016 9:04 pm

Draw a picture of the data - or in this case, a table with rows and columns of appropriate size. That should make the problem more intuitive.

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