# Which one will fill up first puzzle

• DucatiWiz
In summary, the conversation is discussing a puzzle involving filling tanks with water and which tank will fill first. The original problem is an extension of an old water-level puzzle and the answer is that the third tank will fill first. However, there is debate on the forums about the flow rate of the water and whether it could cause a different tank to fill first. Ultimately, there are no specific measurements given to accurately calculate the flow rate and the puzzle is designed to demonstrate how water finds a level in any shape vessel, not the dynamics of water flow. Therefore, the answer remains that the third tank will fill first.
DucatiWiz
Hi all, I'd like as many opinions as possible please as this seemingly simple question has caused quite some discussion on Facebook.

Very grateful for any contributions.

http://www.bikersoracle.com/pics/fillquiz.jpg

First you need to say what YOU think will happen and why

What does it mean to fill up first? Which one is around 90% capacity first? Or which one overflows first? If the flow rate is as high as the image makes it out to be than 1.

The 2 tank first to fill-up

Student100 said:
What does it mean to fill up first? Which one is around 90% capacity first? Or which one overflows first? If the flow rate is as high as the image makes it out to be than 1.

It means to fill, i.e. fill to the brim; 90% isn't full

Ok I didn't know I was supposed to give my opinion. I think the answer is 3

This is merely an extension of an old water-level puzzle that has been done to death on the internet. The puzzle usually stops after the first 4 tanks and the answer is that the third and forth tanks in the sequence fill simultaneously (tanks 2 & 4 in the 6 tank version). See here:

However, in the new variant, tank 4 will not fill as it drains into 3, therefore, tank 3 will fill first. In fact, no other tank will ever fill as the liquid will continue to spill over the rim of tank 3 and the level will never rise above that.

Last edited by a moderator:
DucatiWiz said:
I think the answer is 3 ... tank 4 will not fill as it drains into 3, therefore, tank 3 will fill first. In fact, no other tank will ever fill as the liquid will continue to spill over the rim of tank 3 and the level will never rise above that.
I agree and I don't even see why anyone would think this was much of a problem. Are we missing something?

Well, the argument is that that if the flow from the tap is fast enough to keep 1 full, the additional head of pressure will fill 5 faster and then 2 faster than the water can escape from 2 into 4, therefore 2 will fill first.

pgy1+1/2pv1^2=pgy2+1/2pv2^2

I don't agree, I think the guy arguing that case (who does have a physics degree) is not taking account of the following:
1. The flow from the tap is unknown. If it were high enough, it could fill 1 before it fills 5
2. The exit tube from 2 into 4 will remain at zero pressure because 4 will never fill past the entry point, so the extra speed of flow into 2 would have to be very much higher for it to fill faster than it could exit into 4.
3. There are no specific measurements to calculate an accurate flow rate. The puzzle is designed to demonstrate how water finds a level in any shape vessel or arrangement of tubing, not the dynamics of water flow rate, given pressure, diameter and viscosity. Whilst the tube from 2 to 4 does look thinner, it is not a scale drawing and without any specific measurements, there is no way to know if it would be small enough to cause 2 to fill first.

Again, I agree w/ you. Positing an extra fast water flow does not seem to me to be part of the problem as stated.

phinds said:
Again, I agree w/ you. Positing an extra fast water flow does not seem to me to be part of the problem as stated.

The problem stated is in the picture, in which we clearly see a high rate of flow from the nozzle.

Other iterations normally show a drip, in which case flow out of 1 is balanced with the flow in from the nozzle. Whereas I'm making the assumption here that the flow in >> than flow out of one. It's a problem with the graphics designer if that wasn't meant to be considered.

My assumption is as good as any other. One fills first.

## 1. How does the "Which one will fill up first puzzle" work?

The puzzle is designed to demonstrate the concept of equal rates of change. It consists of two containers, one larger than the other, with a small hole at the bottom of each. When both containers are filled with the same amount of liquid, the smaller container will empty at a faster rate due to its smaller volume.

## 2. What is the purpose of the "Which one will fill up first puzzle"?

The puzzle is often used as a teaching tool in mathematics and science to help students understand the concept of equal rates of change. It can also be used to demonstrate the concept of volume and how it affects the rate at which a container fills or empties.

## 3. Is there a specific strategy for solving the "Which one will fill up first puzzle"?

The puzzle does not have a specific strategy for solving it. The solution is based on understanding the concept of equal rates of change and how volume affects the filling and emptying of containers. It may require some trial and error to find the correct solution.

## 4. Can the "Which one will fill up first puzzle" be solved using mathematics?

Yes, the puzzle can be solved using mathematical equations that involve volume and rates of change. However, it can also be solved by simply observing and understanding the concept of equal rates of change.

## 5. Are there any real-life applications for the "Which one will fill up first puzzle"?

Yes, the concept of equal rates of change and volume has many real-life applications, such as in fluid dynamics, engineering, and economics. Understanding this concept can help in various scenarios, such as determining the most efficient way to fill or empty a tank or calculating the rate of flow in a pipe.

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