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# Brain game from computer science

2 replies to this topic

### #1 antipope

antipope

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Posted 08 July 2014 - 02:37 AM

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?

Spoiler for Hint

You can post the answer in the form RRYGYGR..., where R=red, Y=yellow, G=green.

Edited by antipope, 08 July 2014 - 02:39 AM.

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### #2 k-man

k-man

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Posted 08 July 2014 - 05:06 PM

Spoiler for solution

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### #3 antipope

antipope

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Posted 08 July 2014 - 09:15 PM

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.

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):

Spoiler for Solution

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