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I didn't determine that there were 7 solutions until after I had done them all! The process was something like this:
"Hmmm, I don't see many inferences, but this 'cleanings' restriction looks important, so let me try something. Can I alternate mulch and stone a bunch of times? No, that will be too many cleanings, so I have to keep some clusters of each together. I know an M is 5th, so let me try putting all the Ms together around that spot. How many ways can I do that?"
"Okay, I found a few ways to make that work with the Ms all in a bunch. Now can I try splitting one of them off from the other two? How might that work. This is taking a while, but it feels like there aren't going to be that many more workable solutions, so I am going to keep going with this."
"One more thing to try, and that is leaving that M at 5 all alone, and taking the other two Ms away as a pair since I now know I can't just split them all up, even if I put the other two Ms at 1 and 7. Okay, that only works one way, so I think I'm done! Let's go crush some questions!"
Identify the Possibilities games, where the best solution is to just draw them all out, are few and far between. You should hesitate before going down this path, and often when you start down it you will find yourself either just doing templates or else you will abandon the approach as soon as you realize that there are too many solutions to make it worth chasing them all down. But there will be times, like with this game, when the process should be carried to the end and the results will be very beneficial, leading to a very rapid and completely accurate run through the questions, followed by a little happy dance in your chair!
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