Thursday, June 2, 2011

Is There More To More?

This is a tricky puzzle, yet a trivial one, depending on how you look at it.

You have a container, such as a glass or a bucket. How to fill this container up three times without ever taking anything out of it?

The answer does not include any outside help, evaporation or divine intervention.

Top image by cafemama, distributed under CCL.

Answers accepted all day long on Friday June 3rd and Saturday June 4th, on our Family Puzzle Marathon. They will be hidden until Sunday morning (EST) and everyone who solved it will get a puzzle point. Please, explain your answer.


Katrina said...

You first fill the bucket with rocks, then with sand and finally with water. each time the material will fill the available space but there is room for the next material to be added in the spaces between.

Tom said...

Just leave a hose in it all morning. It will refill several times, probably more than three, and we've taken nothing out of it.

More seriously... "fill it up" with (1) golf balls, then fill the remaining volume with (2) sand or BB's, and finally fill it up again with water.

kj said...

You do not specify what you want to fill the container with -- so I will fill it with three different things.

Your picture of the five gallon utility bucket reminds me of removing rocks from my garden -- so I will first fill the bucket with rocks. (Yes, I live in New England, and our first crop every spring is rocks!)

Is the bucket full? Well, yes and no. We can't fit any more rocks in, but there is plenty of space between the rocks.

Now we will add sand. The sand will fill a lot of the empty space between the rocks. We may need to jostle the bucket to get the sand to settle down to the spaces at the bottom of the bucket, but we'll keep doing this until it is full of sand and rocks and we can't add any more sand.

We can't add any more sand, but we can add water, since there is still space between the grains of sand.

Now we have filled the bucket three times, and we have not removed anything from it (except for the air).

anne-marie said...

First, the rocks.
Second, the sand that will fill out the space between the rocks.
Third, the water.
It is often taken as an example for inspirational stories on time management.
The rocks being the more important things to consider, to prioritize.

Ilya said...

Here is one idea, I am sure there are other possibilities. The big assumption here is that the container does not need to be empty in order to say that it is being "filled up" again. We'll define "fill up" as an action of adding a non-zero amount of certain substance to the container as long as the substance is not overflowing.

1. first fill it up with ice cubes
2. then immediately pour sugar to "fill it up" again.
3. when ice melts, pour water to "fill it up" again.

Alternatively, you can just use three different substances of different granularity - e.g. large balls, smaller balls and then sand.

Lynnet said...

The problem never says: what to fill it with and whether or not you have to be able to recover what you fill it with. So I would use differences in density of liquids. First, I would fill it with cooking oil. Then with water, which would displace the oil and not mix. Last I would pour in molasses, slowly so it doesn't mix, which would displace the water. I would have filled the container 3 times without ever taking anything out.

By the way, I figured this out myself. And I'm a kid!

Homeschool mama said...

I'm new here, but am going to give it a shot. Other than the bucket having a hole for a slow leak, I am wondering if this is about filling it first with big rocks. Then, adding smaller rocks/pebbles. They will fill in some gaps. Lastly, fill with sand? Going to think on this a bit more, too!

Bean said...

First, I will fill it with rocks. Then I will fillet with sand (or maybe salt). Then I will fill it with water.

Or some other combination of things that decrease in granularity...marbles, them B-Bs, then glitter.

SteveGoodman18 said...

Thanks to my wife for some help with this one.

One idea - fill it up with ice, then let the ice melt and fill it up with ice again, then let the ice melt and fill it up with ice one more time.

Another idea - first fill the bucket with rocks, then with pebbles, then with water.

Anonymous said...

It looks like I am finally able to post today. Blogger was unavailable since this morning.

It looks like gardening and product management training came handy to some of you in this puzzle. The key was to realize that the container does not need to be filled with liquid and same content thrice. Rocks, rice and water. Or rocks, marbles and rice. A puzzle point for Katrina, Tom, kj, anne-marie, Ilya, Homeschool mama and Bean.

Steve - I am not sure about the ice solution. Going to try it right now. Lynnet - same about the liquids of different densities. When container is filled to the top with cooking oil, I am not sure one can add anything to it. You all are very creative and wise.


SteveGoodman18 said...

Thanks Maria - I still contributed a correct solution in addition to the ice thought.

Anonymous said...

You are absolutely right, Steve. I was intending to but somehow forgot to give you a point for your second answer. But now I also have a visual proof of your first solution being correct as well. If one uses large pieces of ice, they fill the space of the container like rocks, leaving large gaps in-between. When ice melts, container is no longer full and more ice or water can be added to fill it up again. See this picture of a glass of ice and then same glass with half ice melted a few hours later.


Lynnet said...

If you fill it up with oil and then with water then the water would displace the oil. If you gave a point to Tom for his answer of a hose, then what is wrong with my answer of playing with density. I am in 6th grade science and density is one of the more interesting things talked about this year. If you fill it with rocks, then it isn't really filled because there is still lots of space in the container.

Anonymous said...

Lynnet - you are so sweet! I am giving you a point for just participating and arguing your point through. My son is in 5th grade and I know how brave you should be to play along with the people that are up to 7 times your age. But this all is exactly what makes it very interesting. Everyone brings their backgrounds, passions and outlooks.
By the way, Tom got his point not for the water hose solution that I agree is just a joke but for the second part of his answer - after he says "More seriously."

Stay tuned for the next week puzzle. I have a feeling you will be an expert at it .... unless you use only liquid soap to shower :)

and I have to solve a puzzle why blogger doesn't allow me anymore to post as Maria...

Tom said...

Tom adds a week later:
And to be sure, whenever we add anything to the bucket, we are "taking out" some air.

And there is at least one other idea -- pressurization. If we are allowed, and able, to adequately seal the bucket, we could then fill it with, oh, carbon dioxide in addition to the enclosed air, perhaps up to to 2 atmospheres or more. Then fill it again with any gas, to maybe 3.5 atmospheres; and again to 5 atmospheres. Something like that.

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