Machinarium's Pipe Puzzle
Amanita Design's Machinarium is so many kinds of good. It's a wonderfully crafted point and click adventure puzzle game of surprising length and solid challenge.
I want to talk about one specific puzzle in the game. If you haven't played and have the slightest interest in doing so, you should stop reading right now. Really. The game's great, and I don't want to spoil anything for you. Shoo.
Here's the puzzle. Water flows in to this tangle of pipes at the bottom left and flows out the six pipes at the top. We need to shut off the water to the third pipe—the one with the faint arrow—by closing three of the eleven valves which look sort of like plusses.
The game makes the rules and goal very clear. The trick is we need to figure out which three valves to close off.
This actually turns out to be a lot harder than it looks. In fact, after trying to close a few valves at random, it becomes clear it's difficult to turn off any of the outlet pipes, much less the third one.
I tried logicking my way out, which is a stupid way of spelling thinking about it, but the mess of pipes was just too confusing to keep straight.
I considered brute forcing the puzzle by trying every possible solution, but since there are eleven valves and three wrenches, or in math-speak 11 choose 3 combinations, a quick calculation shows that's still 165 arrangements to try.
Actually it's slightly less, because there's no need to turn off both valves on the right. Still, 120 possible solutions is a lot, and Machinarium is a fair game. I knew there had to be a valid strategy for solving this.
What if we could shut off every valve? If we traced the pipes from the inlet in the bottom left, stopping when we reached any valve, the water would flow through the blue colored pipes. It's interesting to note that it's impossible to shut off water to the second outlet pipe.
Let's do the same thing, but trace backwards from the third outlet, the one we're trying to shut off. I've colored those pipes red.
And then let's overlay these two colorings at the same time. What's interesting is the blue and red meet at two valves. No matter what we do, water will always be flowing through the blue, and no matter what we do we can't let water flow into the red.
From that it's pretty easy to figure out we must place two wrenches where the blue and red pipes meet.
And from there we only have nine places (eight, really) to put the third wrench. It's easy enough to try them all, and the unique solution isn't hard to get.
Just for fun, here's where the water's flowing after those three valves shut off. We didn't turn off the water just to the third pipe, we turned off the water to most of the city!
Machinarium actually contains a full walkthrough in-game. I could have just asked for the solution at any time, but that's not fun at all: the answer isn't interesting, the puzzle and it's strategy is.
Actually there was one part of the game that I used the walkthrough for. I can only conclude that the designer behind the middle arcade machine simply hates people.