antipope

Nice! I wasn't sure if someone would be patient enough to solve this on paper For those of you who liked this, there's a game for Android and this is exactly one level from this game. It's called J-Fizo and you can find it on Google Play if you have Android phone or tablet. If you get to H level, email me at bd@atablash.pl, send me your email address registered with Google Play; I will add you as testers so you can play the rest of the game for free. Let me know how far you got since I don't think anybody can pass this entire game without brute-force computer approach PS Here's k-man's solution in animated GIF form (in fact it is the minimum possible number of moves):

I came up with an idea for a brain game. It's a modification of something called an automaton. Automata theory is a part of theoretical computer science. The game looks like this: You can draw those 5 colored edges on a piece of paper and place 2 pawns at the top 2 vertices. The goal is to end up with only 1 pawn. To reach the goal, you can make moves of 3 types, one type for each color, call it C: When you select color C, you locate every edge with color C such that there is a pawn on one end and there is no pawn on the other end. Let's call these edges C-triggered. Then you move pawns along C-triggered edges: - If there is a pawn adjacent to k C-triggered edges, it splits into k pawns. - If more than one pawn arrives at the same destination, they are merged. In other words, after color C move, every edge that was C-triggered is "swapped"; that is for each end vertex if there was a pawn before, now there isn't and vice versa (note that there is a pawn on exactly one end since edge was C-triggered). Can you solve the problem instance on the picture? What is the minimum number of moves? You can post the answer in the form RRYGYGR..., where R=red, Y=yellow, G=green.

My name's Adam, I live in Poland, I study computer science and I'm here to show you my idea of a very difficult brain game. It looks like this is the place where it could get appreciated. The idea comes from automata theory and the game is extremely difficult for a human, although can be easily solved by brute-force approach so it's something like Sudoku in this context. I will post one instance of the problem to solve in appropriate section on this forum. We'll see if you like it. Actually I've written this game already but I don't want to be banned instantly for spamming you and leave a bad taste, so I won't give you any link and just wait to see if you want it yourself From other stuff, I love algorithms and programming contests like Topcoder or Codeforces. Naturally, I'm interested in math too. I always liked math riddles, this is my favorite: http://en.wikipedia.org/wiki/Monty_Hall_problem

It looks like this problem is not solved yet, is it? According to Wikipedia (and some paper from year 2012) the number you're asking for is larger than **. EDIT: Ok, I think this paper has the solution