r/theydidthemath • u/iiLove_Soda • 1d ago
[Request] Saw this on twitter. I was thinking it was 2, but not sure.
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u/Different_Ice_6975 1d ago
Despite the fact that it may seem to be the most obvious answer, I'm going to say #3. I think that the argument can be made that none of the other tanks will fill up completely to the point of overflowing until #3 does first.
As for #2, it won't fill up completely to the point of overflowing until #4 also fills up to the point of overflowing (assuming that the pipe connecting #2 and #4 is large enough to handle the full flow of water from the faucet). And #4 won't completely fill up to overflowing until #3 does so first.
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u/Second-Creative 1d ago
This.
The reason is that the pipe connecting 2 to 4 has its exit point lower than that of 2 and 4's top.
This means that, due to equilibrium, #2 cannot be completely filled until the water in #4 submerges the exiting pipe. Conversely, this means that #4 won't start filling until the water in #2 reaches the height of the exit point.
Incidentally, only #3 will be completely filled in the setup, as its top is lower than the remaining areas, resulting in the water overfilling #3 and causing a horrible mess.
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u/IAmGiff 1d ago edited 1d ago
Assuming it’s two dimensional 3 and 6 will both fill completely (including the area above the pipes between 3-4 and 3-6) but then the system will drain out the right side of 6 before 4, 2, 5 and 1 ever fill up.
Edit to add: Quite a few people were confused by this. Let me explain more clearly.
The people confused by this all assume the image represents a cross section of 3-dimensional boxes connected by enclosed pipes. Under this assumption, yes, the system drains once box 3 has filled.
Another assumption is this is a two dimensional puzzle. This is also a very simple and logical assumption. It is merely this: Water flows down and cannot flow through lines.
Under this assumption, the first box to fill is 3. Once 3 “overflows” the water pools atop the pipes that connect 3-4 and 3-6. As it continues to overflow, this entire cavity fills until both the cavity and box 6 completely fill. Because water cannot pass through lines it cannot escape the system until Box 6 is filled. Then, the system drains out the right side of box 6.
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u/big_sugi 1d ago
How does 6 ever fill, when the top of 3 is open?
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u/IAmGiff 1d ago
Where does the water go once it goes out the top of 3, in a two-dimensional system?
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u/big_sugi 1d ago
Why are you assuming it’s a two-dimensional system?
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u/gmalivuk 1d ago
Doesn't matter why. The comment pretty clearly stated that assumption.
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u/bigloser42 1d ago
If it’s 2 dimensional, none of them can be filled as none of them have any volume. Having volume requires 3 dimensions.
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u/Omnizoom 1d ago
Yes and no
You can fill a surface area of a plane , yes it’s not a volume but it’s the 2d equivalent of being filled in, so you could have a circle that half filled in
Imagine instead it’s a plane sandwiched between 2 sheets of glass for the aspect of it “filling”
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u/SahuaginDeluge 1d ago
I think this is technically correct, and reddit very often hates technical correctness.
I would also say, it doesn't even have to be literally 2-dimensional for this to work. if the containers are sandwiched between two panels, like an antfarm or many Steve Mould experiments, then 6 will also fill up. we can't really tell from the diagram whether the system is "open" or "closed" in that way.
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u/7heWafer 1d ago
6 will not fill, the waterline will overflow out of the top of 3
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u/IAmGiff 1d ago
Yes, but unless you assume water can flow through some of the black lines, the water will then flood the area above the pipe between 3-4 and the area above the pipe between 3-6. If you assume water can’t flow through black lines, then 6 fills completely.
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u/Platano_con_salami 1d ago
I'll just let u know that it being 2 dimensional or 3 does not change the answer.
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u/IAmGiff 1d ago
The people who don’t understand my point have a valid interpretation of a 3 dimensional system where water can flow “around” the outside of pipes. They are correct that with this interpretation the system drains out of 3. In a 2-dimensional system, however, where water can’t flow through lines then the entire area above the pipes fills up.
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u/Figarotriana 1d ago
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u/shiny_brine 1d ago
Yeah, the connections into and out of #2 do not look similar, so it's going to be dependent on size of the in/out flow of #2 and the initial flow rate as to whether #2 or #3 overfill first.
Dam internet is never specific enough!3
u/sysiphean 1d ago
If we are factoring in flow rate, it could even be #1. The flow into 1 seems a lot more than the flow from 1 to 5.
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u/FirstSineOfMadness 1d ago
My only hesitation is due to pipe size 2 is filling faster than it empties
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u/Puzzleheaded_Way9468 1d ago edited 1d ago
If we're getting into pipe size, it's possible 1 will fill first.
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u/throwaway387190 1d ago
Kinda depends on your definition of "filled"
To the point of over flow? I completely agree with you
But from where I'm looking, the height of the spout on #4 is close enough to full on #2. Like when you fill up your cup of water, you don't consider it full only when it's about to overflow. You leave some room at the top
But the prompt is vague, no way to tell
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u/YoungMaleficent9068 1d ago
I like the fact that with this one there seems to be no stupid tricks like optical illusion or so.
Not even pipe diameter and flow rate things.
As usual the 5 yo creator will appear and let us know what the genius trap was that was set and we all fell for.
Brace yourself for "oh you held it upside down"
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u/BrightRock_TieDye 21h ago
Never would I have considered overflowing to be a requirement for full; the level that 2 must reach before water starts pouring into 4 is what I would consider full. If I'm filling a bucket or a glass or any other vessel for any practice reason, then full is just reasonably close to the top.
However, give. That people seem to be in disagreement on that, I'd have to say that there is insufficient information presented. We need marks on each tank to indicate full, and as others have stated, we need information on flow rates.
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u/Different_Ice_6975 20h ago
It seems that the one thing that people here are nearly unanimous on in response to my post is that it is a poorly presented question.
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u/Spiritual_Prize9108 1d ago
Unless tge static head difference between the top of two and the outlet height of two is less than the dynamic head of the 2 outlet pipe at the mass flow rate through the system.
Therefore insufficient information is provided.
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u/Maumau93 1d ago
The pipe leaving 2 is the narrowest. 2 will fill first.
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u/Different_Ice_6975 1d ago
All depends on whether the pipe is narrow enough to significantly constrict the flow of water from the faucet, and that's not clear from this simple schematic and no information is given on the matter of flow construction by the question. As many people have pointed out, there are problems with the ambiguity and lack of information given by this question.
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u/Traditional-Storm-62 1d ago
if the water is flowing in fast enough it'll be 1
but the legit answer is 3 because its brim is the lowest and all the pipes have both their entry and exit below the brims of their respective tanks
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u/loscacahuates 1d ago edited 17h ago
There's just not enough info to say one way or another. You need pipe sizes, tank dimensions and elevations, and the inflow rate.
Assuming all pipes are the same size, then it depends on the inflow rate. If the flow going from tank 1 to 5 can't keep up with the inflow, then tank 1 will indeed fill first. If the flow is slow enough and the outlet size is big enough to handle that flow for each tank, then it's tank 3...but it takes some assumptions to get there. Also the rate of drainage increases as the depth (or head) in any given tank increases. It's a bogus question.
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u/DannyBoy874 1d ago edited 1d ago
It depends what you mean by “fill”
3 will be the first to overflow.
2 will be the first to appear pretty full as it will fill up to its inlet.
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u/Few-Artichoke-7593 1d ago
"pretty full ass"
Nice
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u/Accomplished-Boot-81 1d ago
That's depends on the water flow, the outlet of 2 is smaller than the inlet, so it's very possible 2 will overflow first if the inflow is quick enough. Also the water pressure from 5 filling 2 will overcome the water pressure from 2 to 4, support this hypothesis further
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u/DannyBoy874 1d ago edited 1d ago
It’s clearly coming out of a tap into 1. If that tap is blasting, 1 will fill and overflow first. If not, which is what I’m assuming, it will be 3 to overflow first as I described.
I think it would be very difficult to find a flow rate by adjusting the tap to make 2 overflow before 1. Either way, that’s a corner case so I’m not assuming that flow rate. If the “problem” wanted flow rate to be taken into account it should have given a flow rate and pipe sizes. Since it didn’t, it’s reasonable to assume that’s not a factor.
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u/dev0guy 1d ago
Water comes out of the tap at a 100000L/s. Nothing fills because it destroys the apparatus. The project manager blames the engineers.
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u/i_like_big_huts 1d ago
We clearly said it's an apparatus of concept made of toast and that it must not come in contact with water
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u/_killer1869_ 1d ago
This entirely depends on the water's flow rate. If it's high enough, number one will be filled first, because it can't flow out quickly enough. Otherwise, it would be two, but with a lower flow rate, two won't be filled completely to the top. With a low flow rate, the first to fill completely would be three.
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u/miguescout 1d ago
Someone did a simulation and, when the flow wasn't high enough to fill 1 first, or slow enough that water had basically no speed, it was 2 that filled to the brim (not only to the top of the exit tube) as the turbulences caused by the high pressure flow from the previous tank into it made it so considerably less water got through to the next tank than entered it, filling it quite quickly
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u/Bitter_Bert 1✓ 1d ago
Disregarding fill rate and flow between tanks, 2 will only fill up to the level of the outlet to 4. I think 3 in this case. If we're supposed to think the flow from 1 to 5 and 5 to 2 is about the same as the flow into 1, then 2 to 4 looks constricted and 2 will fill first.
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u/General_Ginger531 1d ago
Bucket 3, and only Bucket 3. Bucket 5 doesn't get filled because it flows into Bucket 2, because of how water fills the shape from the bottom up, bucket 2 won't fill up because it will flow into bucket 4, essentially using its own water pressure to do so. Bucket 4 won't fill because it has a drain at the bottom that goes to bucket 3. Bucket 3 will fill up to the point where it starts to fill up bucket 6 after filling up the tube between them as it's water level rises, and then because the top of bucket 6 is higher than the top of bucket 3, all of the extra water put into this system will just fall out of bucket 3, never even filling up bucket 6.
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u/IAmGiff 1d ago
If it’s a two dimensional system the water flows out of 3 and floods the area above the pipes that connect 3-4 and 3-6. So 6 also fills completely and the system drains out the right side of 6.
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u/Mr_Arthtato 1d ago
There are only three correct answers based on the flow rate. This is based on the assumption that the pipe size is accurate in the photo above.
There are three scenarios.
The flow rate is faster the drainage between 1 and 5. In that case 1 fills up the first.
The flow rate is slower then the drainage rate between 1 and 5, and 5 and 2. But the flow rate is faster then the drainage between 2 and 4. In that case, 2 fills up first.
The flow rate is slower then any of the drainage rates or the same as the slowest connection (4 to 2). In that case, the first to fill up would be 3.
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u/Ataxari4 1d ago
Bucket 3 must be filled before Bucket 6 can begin to be filled.
I think, it is bucket 3. I can’t prove it logically. But here are my thoughts. Start with a slow rate of flow. All the other buckets fill to the point where they begin filling. By the time all of the buckets up to 3 begin to fill enough to start flowing, assuming a slow rate of flow, 3 would just get all the water flowing.
The only way it’s not Buckets 3 is that the rate of flow out of the buckets is slower than the flow going into the buckets then it is bucket 1.
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u/Doggfite 1d ago
3 doesn't have to be full before 6 begins to be filled, 6 will definitely start to take on water before 3 is full to the top because the highest point of the connection to 6 is below the top of the edge of 3.
You're still correct otherwise.
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u/Tricky_Routine_7952 1d ago
Depends on definition of full, and flow rate. Neither of which we have. Assume it is one of these puzzles that is written deliberately poorly to generate engagement and clicks.
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u/la_rattouille 23h ago
Depends on your definition of fill.
If you mean filled to the brim and spilling, then it's not 2.
But if you mean filled 85% then it's 2.
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u/elkab0ng 1✓ 1d ago
- The water coming out of the faucet shows no narrowing of the stream, meaning it is coming out at full pressure I.e. from a municipal source at ~60psi. The exit conduit from #1, having only the pressure generated by the content of the container, will never be able to empty at the rate the tank is being filled.
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u/Vlad_The_Impellor 1d ago
The connecting tubes are effectively a series of restrictive orifices. To solve the maximum flow rate, we need to know the tube diameter, tube lengths, gravity factor & temperature of the incoming water. A simple quadratic solves for flow rate at each collecting pool.
3 unless we consider whether the incoming flow rate exceeds the connecting tube flow rate.
6 will never fill. This is the only certainty.
Insufficient data.
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u/HesitantInvestor0 1d ago
It's impossible to know without knowing the flow rate.
I'm going with Tank 1 because the flow rate from the tap appears to be higher than the flow rate Tank 1 would provide to Tank 5.
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u/Krmedeiros 1d ago
If the flow is enough won’t bucket one fill up before the water can transfer to the other buckets.
So isn’t this unknowable without knowing the flow rate and size of the connection pipes.
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u/JOliverScott 1d ago
I think it depends on the flow rate of the faucet because every pipe is uniform diameter except from 2 to 4 which appears smaller in diameter. If the flow rate into 1 is fast enough that cannot empty into 5 as fast as it is collecting in 1 then 1 will fill first. If the flow rate is slow enough that pipes 1 to 5 and 5 to 2 can keep up but 2 to 4 cannot then 2 will fill first. If the flow rate is slow enough that even the pipe from 2 to 4 can keep up then 3 will fill up to overflowing first because it has the lowest point of egress in the system.
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u/mortemdeus 1d ago
So, there are only two options. Either 1 overflows first as the outlet of 1 is too small or the flow into 1 is too high or 3 fills because it is the lowest on the system.
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u/Short_Sniper 1d ago
Depends on the flow rate. A higher flow would lead to #1 filling up first. If it’s a slow flow rate #3 would over flow, #2 would fill would be first to reach its 3/4ths fill limit.
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u/DirtyChito 1d ago
They're labeled in the right order.
1 will fill up first because the flow of water is bigger than the outlet. It also has the advantage of start time.
2 will fill up second for the same reason. The water flowing in is through a larger waterway than out. It also won't start losing water until nearly full due to equilibrium.
3 is pulling water in faster than 4 is gaining, so it'd be next. It also will only lose water after a certain time and for a certain time.
4 can't fill up until 3 is nearly full. This is the only one that may be wrong. 5 may beat it.
5 looks like it is losing water at a slightly faster rate than gaining, so it'll need 2 past the fill path before it'll really be gaining water at a decent rate.
6 may never fill up. Since there will be more pressure pushing down on 6 as it fills than 3 will have to push uphill, it's more likely 3 will overflow before 6 gets halfway.
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u/Mysterious_Bid3920 1d ago
3 , The top of 3 is closest to the bottom. It doesn't matter how they are connected, only which one's brim is closest to the center of gravity
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u/el-waldinio 1d ago
Anyone one know why these diagrams have become so popular in recent years? Various versions have been popping up on FB/Twitter etc for the last few years.
Are they being used in job applications/school tests or something like that?
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u/LeCataire 1d ago
It's because they generate a lot of engagement.
Since there is a lot of missing information, every one state their advice and the posts have a high flow of answers and debate.
As long as engagement farminng goes, this is quite similar to posts with PEDMAS problems, even if PEDMAS operations usually have a definite solution.
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u/Pretend_Buy143 1d ago
2 will fill up first because it's exit is on the same level as the input.
No water will pass through to 4, 3, and 6 until 2 fills completely.
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u/Reqrium_lost 1d ago
None of you are considering the fact that (assuming it’s to scale) the opening to the faucet is larger than the pipes leading out of the containers. Meaning if you fill the first one faster than it can be syphoned off the first one will fill first.
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u/SomeoneElseYouKnew 20h ago
I’m eye balling this, so be gentle. But, I think tank1. The flow rate of the source appears to be twice that of the connecting pipes. Therefore, 1 will over flow before the other downstream tanks will fill to the point of breach.
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u/cr8zyfoo 20h ago
Mathematically, #3. According to fluid dynamics, however, #1. Even though #1 has a hole in it, the flow rate from the faucet is much higher than the flow rate possible through the pipe connecting #1 to #5, and #1 will continue to fill even while being drained. Given enough water pressure at the tap, #1 will fill before enough gravity powered flow can reach and fill #3. Since the water flowing from the tap is at an angle AND does not show curvature due to gravity, it clearly has an extremely high flow rate.
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u/N5022N122 23h ago
no the answer is the first one. There is no indication of the flow rate. If fast then the first one will fill quicker than the water going out the tube to the next and this overflow.
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u/rudiseeker 1d ago
Tank 3 will fill up first. Given the following:
The tops of all the tanks are higher than their respective entry and exit points.
The entry point of tank 4 is level with the exit point of 2.
The rate of flow of the water is slow enough to not be a factor.
Tank 4 will start filling once the water in tank 2 reaches its exit pipe. Tank 3 will fill until the water level in tank 6 is level with the top of tank 3. Then tank 3 will start to overflow.
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u/Commercial-Act2813 1d ago
1 will fill first, as it is directly under the tap.
It will not become full, but will start to overflow into 5 through the connecting pipe, making 5 fill second, etc.
3 will fill completely till the point of overflowing over the rim.
All the others will remain only partially full and keep overflowing through the connecting pipes.
2 will be at the highest level other than 3 and could be considered ‘full’, but it will not be to the rim.
It will fill up to that level before 3 starts to fill.
So depending on what you think ‘fill’ and ‘full’ mean, it is either 1,2 or 3
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u/oynutta 1d ago
Depends on the volume of water coming out the pipe and the volume of water that can fit through each tube.
It's possible #1 fills up first if the faucet is giving 1 gallon / min but the tube connecting 1 to 5 only allows 0.01 gallons / min.
But let's assume the water fills so slowly that the water amount doesn't matter. Assume the faucet slowly drips and the tubes are wide enough.
Then it's #3.
1 will fill last as it is highest.
5 will fill second-last as it is 2nd highest
As water slowly goes into #2, eventually it spills into #4 and keeps going as long as water comes from the faucet. All the water going into #4 just spills into #3 first.
Nothing escapes 3 until it is full. As 3 starts to fill, some of it will go into 6. But the water will still level, so as 6 is filling up the water level eventually reaches the top of 3 and starts to spill out. 3 is the first filled and the first to spill out.
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u/underwear11 1d ago
It depends on the flow rate of the faucet. If the flow rate of the faucet is greater than the capacity of the connection between 1 & 2, then 1 will fill up first. If it's less or equal than all the interconnects, then 3 will overflow first.
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u/MisterProfGuy 1d ago
It either 1 or three. Without knowing the rate of flow, the naive answer is 3 from a physics standpoint, assuming that rate of flow is not excessively larger than the rate of flow between pipes. Visually, 1 is filling at a rate that it might overflow before 3 fills.
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u/rrwaaaawrr 1d ago
The only thing that makes this "hard" is the fact that 'filled' is not defined properly. If it said overfilled, then it would obviously be 3. but 2 will be mostly filled first.
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u/Stunning-Dirt-2074 1d ago
To determine which tank will fill first, let’s follow the path of the water: 1. Tank 1 is being filled directly from the tap. 2. Tank 1 has two outlets: • One to Tank 2. • One to Tank 5, but this outlet is higher than the top edge of Tank 1, so water cannot flow to Tank 5 until Tank 1 is full — which won’t happen first. 3. Water flows from Tank 1 to Tank 2. 4. Tank 2 has two outlets: • One to Tank 3 (lower pipe). • One to Tank 4, but the pipe to Tank 4 is blocked — the pipe is higher up, so it won’t receive water unless Tank 2 fills up high enough, which it won’t because water will drain into Tank 3 first. 5. Water flows directly into Tank 3 from Tank 2.
Conclusion: Tank 3 will fill first.
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u/123qwe123qwe123ewq 1d ago
Depends on how fast the water is coming out of the Spicket , if the water is coming in faster then it exits the tank then two is the winner
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u/KiraTheChosen 1d ago
If the faucet flow rate is greater than the exit pipe into 5, 1 would fill first. If not: If the top of the pipe from 2 into 4 is considered high enough to be “full”, then it would be 2. If not: it would be 3 since the actual top of 3 will match the water level in 6 eventually, before 6 is filled.
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u/GamerExecChef 1d ago
Depends how you define "full". 2 will fill up about 80% before filling up 3, and most people would casually refer to a tank that is 80% full, as "full"
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u/0le_Hickory 1d ago
Are we assuming head loss in the pipe? If there is any head loss then it will be 2. If we assume no head losses which is really improbable, the 3.
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u/QuothThe2ToedSloth 1d ago
Wouldn't it depend on the pressure at the tap?
If the water is coming out fast enough then cup 1 is going to overflow before it can drain into 5, right?
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u/EconomySeason2416 1d ago edited 1d ago
Number 1 because the scale is tiny and there isn't enough pressure to allow the water into the pipes? Could someone do the math on how small that would have to be?
Edit: evidently the number sign before a number will change the font size
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u/SoMuchSpentBrass 1d ago
The overflow will occur in either tank 1, 2, or 3 depending on the flow rate from the spigot into tank 1. For very high flow rates (where the flow into tank 1 is significantly higher than can be accommodated by the flow into tank 5), tank 1 will overflow first. For relatively low flow rates, where the flow into tank 1 does not significantly exceed any of the inter-tank flows, tank 3 will fill first. Given the apparent size difference between the entry into tank two and its exit, and the fact that the exit from tank two is effectively near the tank's top, there will likely be a middle volume flow rate into tank 1 where the flow into tank 2 exceeds the flow rate out, and tank 2 fills first.
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u/HeroBrine0907 1d ago
2 will almost fill up, but the water in the pipe will be high enough to pour into 4 before 2 can fully fill up. From there it'll go to 3. 3 WILL fill up because 6 is on a higher level and by the time 6 is halfway filled, 3 will be overflowing.
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u/Major_Growth_918 1d ago
I'm actually concerned about the think pieces that say anything but 2. Because the flow drain from 4 to 2 has to go up unless there is higher pressure in tank 2 pushing into 4, then 2 will fill and overflow. The water will never flow into 4 unless high pressure pushes it in there which would be the filling of 2 in this case which only may be enough to push the water up and into 4.
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u/Andrea2De 1d ago
The tank n. 1, Because more water enters from faucet no. 1 than what flows out through the pipe, as the outflow rate from the pipe is lower than the inflow from the faucet
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u/DonaIdTrurnp 1d ago
It depends on what “fill” means. 1 gets water first, 2 gets about 80% of maximum capacity first, 3 overfills first (assuming all pipes are large enough to move the incoming water with a low pressure differential.
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u/Fantastic-Belt-6077 1d ago
it the whole thing moving? Are the boxes stable? can water run out to the front or back, are there any leaks not visible in the drawing?
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u/Huskerschu 22h ago
It's hard to tell but could even be 1 of the flow rate differential is high enough. If water is flowing into 1 from the faucet faster than it can flow through the small diameter pipe.
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u/Intelligent-Grape137 22h ago
I’m arguing 2 based off the fact that the pipe going in is substantially larger than the pipe going out and will move more water. The exit pipe won’t be able to keep up and the water fill 2 before 3.
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