# Quick brainteaser - Unknown objects and liquid volume/height

• I
• rwooduk
In summary, the conversation discusses a brain teaser involving 3 objects in sealed boxes and using water to determine which object is in each box. There are some difficulties understanding the problem and determining a solution, but it is suggested to use the equations for volume and observe the speed at which the water level rises. It is also mentioned that there may be some tricky cases with floating objects.
rwooduk
Hi, here's a quick brain teaser, if we have 3 objects in sealed boxes, we know what the objects could be: a solid metal cylinder, a metal sphere, mixed shape beads, a beaker with a metal object in it, a pyramid.

We can pour water into the boxes and measure the relative liquid height between boxes.

So how would you determine which object was in each box?

Has anyone done this experiment before?

Last edited:
rwooduk said:
if we have 3 objects in sealed boxes, we know what the objects could be: a solid metal cylinder, a metal sphere, mixed shape beads, a beaker with a metal object in it, a pyramid.
Hi rwooduk:
I am having some troubles with the brainteasers.
I am having a bit of counting trouble. I count 3 objects in the list, not 3.
I am having a bit of visualization trouble. When the water is poured into the box with the beaker, does the water get into the beaker?
I am having trouble with the sequence of events. Does water come out the bottom as soon as water goes into the top? If not, what is the delay? Is one to consider the changes with respect to time among the various water heights?​

Over all, I don't think I understand the problem statement well enough to know how to think about a solution.

Regards,
Buzz

me too have the trouble to understand.

What is the meaning of "sealed boxes" if you can pour water in them?
Can you give a ling to the original text of the problem?

Buzz Bloom said:
Hi rwooduk:
I am having some troubles with the brainteasers.
I am having a bit of counting trouble. I count 3 objects in the list, not 3.
I am having a bit of visualization trouble. When the water is poured into the box with the beaker, does the water get into the beaker?
I am having trouble with the sequence of events. Does water come out the bottom as soon as water goes into the top? If not, what is the delay? Is one to consider the changes with respect to time among the various water heights?​

Over all, I don't think I understand the problem statement

Regards,
Buzz

1. the objects could be any shape, but there is a list of possibilities, the ones given were just a few examples
2. the water goes either outside or inside the beaker, the beaker could be anywhere in the box, under the water inlet or not
3. the tap at the bottom of the box is closed, and the volume of liquid measured changes as you fill the boxes. the water can be emptied at any point by opening the tap at the bottom.
4. Yes, I believe that is the theory, to watch the water level and how it behaves, for example if it rises quickly there is a large object in the box. If it rises slowly, there is a small object, if it doesn't rise at all until a certain point then it is going into a beaker first etc etc

I just wondered if there is a way to quantify this? i.e. knowing the equations for volume of the objects

Other than that I will have to simply have the students watch how the volume level of the water rises.

nasu said:
What is the meaning of "sealed boxes" if you can pour water in them?
Can you give a ling to the original text of the problem?

You can't see inside the boxes, they are metal and just have a water inlet and outlet taps.
Afraid I don't have one, I've been asked to demonstrate this thing and it seems pointless as nothing can be quantified! It's only for first year students, probably just for a bit of fun, but in my first year physics experiments we were doing errors, analysing lasers, magnetic fields etcetc everything was quantified and analysed.

Thanks for the replies.

Buzz Bloom
rwooduk said:
I just wondered if there is a way to quantify this?
You can compute the volume unoccupied by the objects for horizontal slices, which tells you how fast the water level rises at the height of each slice.

But there are tricky cases: The entire beaker interior belongs to the slice at the top of the beaker: Big slow down in level rise at this point, easy to spot.

I'm assuming the objects don't float.

A.T. said:
You can compute the volume unoccupied by the objects for horizontal slices, which tells you how fast the water level rises at the height of each slice.

But there are tricky cases: The entire beaker interior belongs to the slice at the top of the beaker: Big slow down in level rise at this point, easy to spot.

I'm assuming the objects don't float.

Good idea! Thanks for that.

Unfortunately there are some different sized hollow balls that do float.

rwooduk said:
Good idea! Thanks for that.

Unfortunately there are some different sized hollow balls that do float.
While all the objects inside float, the level rises at a constant rate that is equal to the fill rate. The offset between the filled in water volume, and what the level says is determined by the weight of the floating objects.

However there are transition phases at the begin (nor floating yet) and the end (ceiling contact). If you have too many objects, they might not float freely for long.

rwooduk
A.T. said:
While all the objects inside float, the level rises at a constant rate that is equal to the fill rate. The offset between the filled in water volume, and what the level says is determined by the weight of the floating objects.

However there are transition phases at the begin (nor floating yet) and the end (ceiling contact). If you have too many objects, they might not float freely for long.

Great, that really helps! Thanks again.

## 1. What is the purpose of this brainteaser?

The purpose of this brainteaser is to test your problem-solving skills and critical thinking abilities. It involves using information about unknown objects and liquid volume/height to come up with a logical solution.

## 2. What information do I need to solve this brainteaser?

You will need to know the volume of the unknown objects and the height of the liquid in order to solve this brainteaser. It may also be helpful to know the density of the liquid and the dimensions of the container.

## 3. Can I use any tools or resources to solve this brainteaser?

No, this brainteaser is designed to be solved without the use of any tools or resources. It is meant to be a mental exercise that relies on your own knowledge and problem-solving abilities.

## 4. Are there any specific strategies or techniques I should use to solve this brainteaser?

There are many different strategies that can be used to solve this brainteaser, and it ultimately depends on your own approach to problem-solving. However, some common techniques include breaking the problem down into smaller parts, using trial and error, and looking for patterns or relationships between the given information.

## 5. Is there only one correct solution to this brainteaser?

No, there may be multiple ways to solve this brainteaser depending on your approach and assumptions. However, there is typically one most logical and efficient solution that can be reached using the given information.

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