Saw a description of climate change effects as "biblical in scale" and my first thought was: Man, if only. Nearly everything in the Bible happens in the middle east. There's really only three global events in the whole thing: the creation, the flood, and the apocalypse. Together, they take up like six pages.
Hit a major breakthrough in Baba today! Finally executed a wild notion in the Depths that seemed necessary for progress but had me stumped for days. This opened up a whole bunch of other levels.
Now I've solved every level I've seen, but the game's visuals seem to be telling me that I have puzzles yet unsolved in both Depths and ???. Hmm.
In a way, F2P games invert the relationship between player and game. In a traditional single-player game, the game judges the players: it presents challenges and the players try to prove that they're capable of handling them. But F2P is about the game continually submitting itself to the players' judgment, trying to establish itself worthy of their dollars.
Imagine a world where the automotive industry is set up primarily to serve race car drivers. You'd go to a car dealership and they'd try to convince you that a formula 1 car better suits your needs than the compact you had your eye on. Or you'd go online looking for recommendations about tires and the top-rated ones are all extremely light and good for high acceleration but can't be used on even slightly bumpy roads.
That's kind of what it's like to be a bicycle commuter.
Actually, there's a bit of a hole in my logic there. If there's exactly one stone remaining in a heap when the other two are exhausted, that heap was not necessarily the largest at every step.
But! In the 3D chessboard formulation, this will never happen, because that would mean that the total distance was odd, which means that the start and end positions were on opposite colors. So add the restriction that the total number of stones in the heaps must be even and we're good.
In the latter case, because one heap still has stones, it must have been the largest heap all along -- which means that you removed a stone from it at every step. The remaining steps will simply remove one stone from it. Since every step removes one stone from the largest heap, the number of total steps is simply the size of the largest heap -- max(A, B, C). And it should be clear that you can't get any lower than the minimum number of steps it takes to exhaust the largest heap.
At each step you should remove a stone from each of the two largest heaps. Eventually you will either have removed all the stones, or you will not be able to to this because you have only one heap with any stones remaining.
In the former case, you have removed (A+B+C) stones at a rate of two stones per step, so you have taken (A+B+C)/2 steps. And it should be clear that you could not have done it more efficiently.
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Y'know, in the unlikely event that the Mueller report clears Trump of all wrongdoing, I'm going to believe it. It would mean that various of his associates who have already pled guilty kept Trump himself out of the loop, but that's certainly imaginable.
But even in that unlikely event, I won't say "I was wrong to have ever doubted him" or anything like that. Whatever happens, doubting Trump was still totally the right call at the time.
An equivalent question: You have three heaps of stones. Call the number of stones in the heaps A, B, and C. A step consists of removing one stone from up to two heaps. How many steps are required to remove all the stones?
(I find it interesting how my intuition changes with how the problem is described.)
OK Mastodon, I have a little math puzzle for you.
Say you have a 3D chessboard, cubes alternating black and white, so that every cube bordering a black cube along a face is white and vice versa. And you have a piece that’s like a bishop with a range of 1 — it can move 1 space in any direction that leaves it on the same color as it started. If this piece is at (x1, y1, z1), how many moves will it need to reach (x2, y2, z2)? (Assuming those are the same color.)
Baba is You, level 3.10, "Further Fields". The solution I came up with was weird and convoluted enough that I suspected it wasn't the intended one. So I did a search online and found a video labeled "Further Fields - Weirdo Alternate Solution".
I think my solution was weirder than the one in that video.
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