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Showing posts from October, 2014

### Problem discussion: Timus OJ 1225 Flags

This was one of the interesting problems I solved last week. I was just checking out Timus OJ when I stumbled across it. Here is the abridged problem statement (read the original statement at Timus OJ): Given $$n$$, the number of stripes, find the number of distinct ways the stripes can be colored if the only colors that can be used are white, blue and red. These constraints should be satisfied: No two consecutive stripes should be of the same color A blue stripe must always be between a red and a white one or a white and a red one. If you want to try to come up with a solution yourself first, now is a good time. I am going to explain my solution in the next paragraph. If you want to submit your solution you need to register at http://acm.timus.ru . The first thing to notice is that the last stripe cannot be blue since a blue stripe can appear only between a red and a white stripe. So, the solution to the problem is \[\text{number of ways in which red is last + number o