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De-duct-ive reasoning

I enjoy puzzles and problem-solving exercises, and I enjoy trying to think like a scientist or a detective.  Recently I came upon a bit of a puzzle outside my apartment, and spent some time applying a bit of forensic analysis, as it were, to the problem.  I have no idea if my solution is correct, but it’s the process that’s the fun part.

A couple of weeks back, we were getting buried under snowfall after snowfall.  One day, I was startled by a very loud noise of something hitting the balcony above mine, and caught an unclear glimpse of something falling.  For a moment, I feared the tree outside, or maybe even the third-floor balcony, might’ve given way under the weight of the snow and ice.  Going outside to check, I discovered it was simply the vertical drainpipe coming down the side of the building from the rain gutters — three stories’ worth and weighted down with ice.

So there wasn’t much mystery as to why it had collapsed.  But a couple of days back, once the weather was warm enough to go out on my balcony again, I was able to take a good look at the fallen drainpipe segments, which haven’t yet been cleared away or replaced.  Here’s what I saw:

Upper part of pipes

Middle part of pipes

Lower part of pipes (Click on images to enlarge.)

Let’s call the longest pipe, the one that’s bent over in the top image, Piece A; the shorter one next to it Piece B; and the shortest piece down in the gravel Piece C.

Now, what I wanted to figure out was: which piece was which?  Which was the top piece, which the middle, and which the bottom?  What order had they landed in and how did they end up in this configuration?

My initial thought was that, since the top end of Piece A was close to the base of the drainpipe, it must’ve been connected there.  I figured that the whole thing toppled over, that the top piece C had come loose and fallen straight down, while the longer piece AB had tipped over, hit the balcony, and broken apart into A and B, with A bending near the bottom and falling down at an angle while B, knocked off by the balcony railing, flipped backward and landed at roughly a 180-degree angle relative to Piece A, crushing one end of piece C when it fell atop it, and crumpling in the middle when it hit the wall as seen in the middle image.  Then the bottom part of piece A must’ve torn free from the base and settled where it’s seen above.

But as I studied the scene further, I realized there were several problems with that hypothesis.  We can be sure Piece C landed first, since one end of it is crushed under Piece B.  But why would the top piece, the one with the farthest to fall, land first?  Also, though it’s hard to tell from the angle of the lower picture, Piece B is slightly under Piece A, suggesting it landed first.  But, I thought, if Piece A was the bottom piece and broke free of its base last, it would’ve had to bend outward and maybe overlap Piece B.

However: I saw no sign of dents on Piece B, or on the (current) bottom part of Piece A.  My working hypothesis was that those two pieces had been joined at the parts that are now down at the bottom, but there’s no damage in that section to suggest an impact with the balcony rail.  The only damage to Piece B is the crumple in the middle and a scrape a little further down, but the crumple was evidently the result of its landing, bending on impact with the concrete wall.

But look at Piece A in the top image.  Just below the top of the stone wall, there’s an indentation in it.  At first blush it seems like it might be another crumple incurred from bending, but look at the very top of the indentation.  It’s too sharply caved in to be just a crumple, I believe.  I’m pretty sure it’s a dent.  That must be where the pipe hit the railing.  And that means that end of Piece A couldn’t have been the bottom end of the pipe.  My initial hypothesis was busted.

But if it was the top piece or the middle piece, how the heck did it end up in that configuration?  And if that dent was the result of it hitting the balcony rail, how’d it end up all the way over there?

I found a clue down at the other end of Piece A, as seen in the bottom image.  That end isn’t just resting atop the gravel — it’s dug into it and has left a bit of a groove behind it.  That means that end couldn’t have started out up top, tilted over, and just landed there.  It had to hit the ground first, driven in by the weight of the whole pipe.

Looking closely at the upper end of Piece A, the one now closest to the pipe base, I see it’s kind of torn open and bent out.  That’s consistent with it being the top end, torn open by the weight of the ice.  And if you look at the left-hand end of Piece C (the shortest one) in the bottom image, it looks like it has a bit of white encrusted around it — like the cement in the base of the drainpipe.

So here’s what I think happened.  Piece A was the top piece, Piece B the middle, Piece C the bottom.  The top end of the drainpipe, weighted down by a great deal of accumulated ice inside and out, tore free, and the whole top-heavy thing started tilting out and to the left (as seen by a hypothetical observer looking at the wall of the building from outside), toward the balconies.  It impacted a balcony rail and sustained a dent.  Its upper half pivoted around that point of impact, pulling Piece AB apart from C.  Piece C, with the shortest distance to fall, landed first.  Piece B hit the next balcony down and sustained a scrape from the concrete balcony edge, but suffered less damage since it hit with less force.  It separated before or during this impact and maybe pivoted a bit around the point of contact with the balcony, possibly causing the clang against my own balcony railing lower down that I think I remember hearing.  Thus, it bounced back to the right and fell at an angle, landing with enough force to crush the end of Piece C beneath it and crumple when it landed in its current position.  (I don’t believe it could’ve landed vertically bottom-first and tilted rightward to settle atop piece C, since the crushing of Piece C’s end suggests Piece B landed atop it with some force.  Similarly with the buckling in the middle of Piece B — that suggests the whole thing landed at pretty much that angle with some force.)  Then Piece A fell nearly straight down, dug into the gravel like a vaulting pole, and tipped to the right.  When it hit the stone wall near its upper end, just above the dent, the momentum of the top portion caused it to whip forward and double over, with the top of the whole drainpipe ending up very near where its bottom was supposed to be.

Okay, that sounds rather complicated.  But it’s a better fit to the evidence than my first hypothesis.  I think it’s plausible, though I’m unsure about a few of the details.  But at least I’m reasonably sure I’ve got the order of the pieces right — A was the top of the pipe, C the bottom.  I can’t see any other way it could go.

All in all, a totally inconsequential mystery, but a challenging one, and thus a nice bit of exercise for the deductive muscles.

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