"The barrels have up down arrows" Nah bro, those are diamonds with a coincidental stripe. There are diamonds all over in the start of the zone.

The programmer of the sonic 3 barrel, the guy who designed the fake dungeon walls in Zelda 2, and the guy who programmed the tornado that carries you to the top of the cliff in Castlevania 2 walk into a bar.
The bartender asks them what they'll be having but they just stare at him with intense eyes until he makes the correct beverage for each of them through trial and error.

The problem was that you get on the barrel and it fools you to think up and down inertia is at play. The whole game works with inertia, then you get to this one tiny part in the game and it uses mind telepathy. It goes against the game's normal gameplay. This part has in the past frustrated me, but I'm at peace with it now.

I like how sonic is spinning while on the barrel. Early 90’s kid in me: Look Sonic is in 3D, wow!!!

My favorite memory playing Sonic 3 when I was a kid, was handing my controller over to my dad who spent so much time trying to figure it out. I was in the kitchen getting a snack and my dad calls me into the living room yelling he figured it out. We got so excited. I lost my dad in 2005, and have a fond connection to that barrel to my dad now

Water shield could let you brute-force your way through the barrel without figuring out Down-Up.

I think a good solution would be to make either the barrel sprite itself, or some arrow panels in the walls react to the up and down input. Press up, and the up-arrows of the barrel light up yellow. Press down, and the down arrows light up. At least that way there would be some feedback that the D-pad input is doing something.

I think the problem also is that even the "correct" solution feels wrong, it should have been jumping

You can actually get passed it from jumping too, further salt in the wound if a friend did it the hard way

I feel so accomplished figuring out to press up and down immediately by myself on Sonic's Classic Collection

This and Psychomantis were probably my two most frustrating gaming moments growing up

My dumbass thought you were supposed to jump under it if it goes high enough with a short jump off

The whole game, the whole series even, has used Sonic's speed as the primary motivator for progress, using his momentum, and building up said moment.
We've played Spring Yard where you had to use the ramps to gain extra height by rolling back and forth.
We've played Casino Night where the way in which you hit the bouncy obstacles while moving through the air was the most important thing for your trajectory.
When we hit Carnival Night, and landed on the first box, and saw it bounce, it was immediately filed into the "Momentum Object" category; this object exists to respond to and interact with our momentum when we land on/against it. The box continues to act this way as we see it more in the level, at no point is it in a position where we might be inclined to stand motionless on it, since, again, it is explicitly reacting to our collision and momentum with it. It is a momentum object.

So when we hit That Box, one of two things happens... Either you have a mind that can easily move things from one category to another, or you don't.
If you do, then you flail at the box a bit, fail, then try inputs that wouldn't make sense for a momentum object, see it work, and recategorize the box as a "Push/Pull Object".
If you don't, you flail at the box, fail, flail at the box, fail, flail harder at the box, fail, and never try the inputs that would succeed, because it doesn't make sense to stand stationary and press directional buttons on a Momentum Object; you simply never think to do so, because that isn't what you do with that kind of object. And while you flail, the box continues to ACT LIKE a Momentum Object, reinforcing the category you put it in.
Eventually, while playing as Sonic + Tails, you might get the bright idea to plug in a Player 2 controller and get Sonic and Tails to both jump on the box in very particular timing to get the box low enough, and the fact that THIS WORKS (albeit barely) makes you feel momentarily triumphant. The idea of a two-character-required momentum object puzzle hasn't really happened before, but it does, when you get there, feel like it 'made sense', even if it was a little bullshit. Of course, playing as a solo character, there is no way to do this, but maybe you don't think about this for now.
The point is, you got past the bouncy box, and can play more of the game.

Later on, you encounter some part of the flow of game information, the trips and tricks, the schoolyard talk, etc. At some point, The Box comes up, and you learn about the push-up-and-down solution and you think "That can't possibly be right. It's too simple. Surely I tried that, right?"
You go back to your copy of Sonic 3, stand on That Box, push up and down, and feel really, really stupid for overcomplicating what is barely any sort of puzzle at all, doesn't even look like it was meant to be a puzzle at that point.
But hey, now you can actually beat Sonic 3 with Sonic Only or Tails Only (or beat Sonic 3 & Knuckles with Knuckles Only!)
So it works out, in the end.

To my mind, the simple solution would have been to take the momentum out of that particular type of barrel. The ones that go horizontally already don't have it, so it's not entirely unexpected. You'd run into the room, jump on the barrel, nothing happens, and then you'd start mucking about with the D-pad. Seeing any kind of movement from the barrel would immediately tell you that you're doing the right thing.

Incidentally, I only knew how to get past this bit from a Mega Drive magazine that came out one after the Sonic 3 guide was printed. This was a mapped guide, so you'd literally see the whole map with little pointers with info boxes for particular bits. One part that didn't get a marker AT ALL was this particular barrel, so it didn't help whatsoever. It was only in the next issue, where someone had written into the magazine to ask them about it specifically, that they admitted the error and explained how it worked. (along with typical-at-the-time-banter that the one who wrote the guide had been appropriately beaten)

I was very lucky that I'd only gotten to that bit when that magazine had just come out, so giving up on the barrel after some fruitless minutes jumping, I went off to read the magazine instead and immediately found out what to do!

My "How was I supposed to know?" moment was the final puzzle room in Alex Kidd in Miracle World.
Halfway through the game you get a stone slab, which you can inspect on the Pause menu, and it shows a whole sequence of symbols including stars, moons, suns and fishes.
So at the end of the game you enter a puzzle room, where you see floor tiles with the same symbols on them. If you stand on the wrong one, a ghost pops out to kill you.
If you're a little clever, this is where you think, "Oh, this must be what the stone slab is for."
And sure enough, it is. Except if you play the game outside of Japan, you start out with a disadvantage, because the sequence is shown in the Japanese reading order; Up to down, from right to left.
Luckily, you do get a sound confirmation when you step on the right panel, so my mother and I eventually managed to brute force the puzzle, but still, it's not exactly explained intuitively for those outside of Japan.

8 year old me timed out so many times on that damn thing. I got passed it (fluke), but figured i just got the jump timing right (was probably pressing up and down as well). Wouldn’t be till many years later it clicked during a replay. I remember getting so ticked off at Tails for messing up the momentum.

I still remember first time I've got to Ice Cap zone after surpassing the barrel for the first time in hundred tries and time out dies. Amazing feeling skiing downhill, as if I was Sonic skiing... What a joyful moment. I used to bruteforce with water shield to bypass the barrel, but sometimes ended up trapped on the wall just waiting for one more death.

if I remember correctly the worst part is that if you mix both you get down low enough but you can't jump off quickly enough to fit in the gap. And mixing it is an intuitive reaction.

You jump on it, it doesn't go down enough. So you jump on it and push down, now it goes a bit further. Do it a few times and you get level with the path at the bottom. So it reinforces the idea that you are doing the right thing but not quickly/well enough. Then it is even harder to realize that you are not supposed to jump, but only look up and down.

Luckily as a kid I somehow managed to glitch through the barrel. It wasn't until I was in college that I figured out how to work the barrel properly.

OK but you cannot just introduce that "someone asked Yuji Naka about this" without even following up on the response!

As a young kid still in elementary school it took me just seconds to understand the barrel