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        riddles >> easy >> Water Buckets - eco version
        
(Message started by: playful on Apr 19th, 2016, 9:35pm)
Title: Water Buckets - eco version
Post by playful on Apr 19th, 2016, 9:35pm
Here is an easy problem with a long introduction.

You know the water bucket problem from the Medium page (https://www.ocf.berkeley.edu/~wwu/riddles/medium.shtml)? (Yes, everyone agrees it would be happier on the easy page.)

Using only a 5-gallon bucket and a 3-gallon bucket, put exactly four gallons of water in the 5-gallon bucket.
(Assume you have an infinite supply of water. No measurement markings on the buckets.)

The orthodox solution requires you to pour ten gallons from the tap and to throw three gallons away.

As an eco-alternative, I wanted to suggest a version of the problem that assumes the buckets are cylindrical, the solution of which would refer to the Glass Half Full problem from the Easy page (https://www.ocf.berkeley.edu/~wwu/riddles/easy.shtml).

But I saw that one of the solutions to this version has already been discussed (https://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1027808333;start=2#2) a long time ago.

This requires pouring eight gallons from the tap, and wasting four. Even more wasteful.

So it seems fitting to leave the following easy question so the answer is shown somewhere on the site for the record:

What is a similar method that only requires pouring 5.5 liters from the tap, and only wasting 1.5 liters?
Title: Re: Water Buckets - eco version
Post by rmsgrey on Apr 20th, 2016, 9:19am
No idea what the 5.5 litre version is, but I can do it with 4.5, discarding just 0.5 litres.
Title: Re: Water Buckets - eco version
Post by towr on Apr 20th, 2016, 10:07am
? [hide]Why not just fill the buckets tilted? 2.5 + 1.5 = 4[/hide]
Title: Re: Water Buckets - eco version
Post by playful on Apr 20th, 2016, 12:39pm
@towr Awesome, that must be the most eco-friendly solution of all!

@rmsgrey That could be better than what I had in mind, depending on what you mean by discard. My "wasted" 1.5L are wasted in the sense that they sit in a bucket at the end without being used at that time, but they don't get thrown out. They lock up a bucket and might evaporate.

What's your procedure?

Here's mine: [hide]fill the 5-liter bucket, do the glass half full trick to the 3-liter bucket, leaving 2.5 in the big one. Top up the small one with 0.5L (total usage 5.5L), then do the glass half full trick to the big one, leaving 4L in the big one and an unneeded 1.5L in the small one.[/hide]
Title: Re: Water Buckets - eco version
Post by rmsgrey on Apr 21st, 2016, 6:39am

on 04/20/16 at 12:39:47, playful wrote:
@towr Awesome, that must be the most eco-friendly solution of all!

@rmsgrey That could be better than what I had in mind, depending on what you mean by discard. My "wasted" 1.5L are wasted in the sense that they sit in a bucket at the end without being used at that time, but they don't get thrown out. They lock up a bucket and might evaporate.

What's your procedure?

Here's mine: [hide]fill the 5-liter bucket, do the glass half full trick to the 3-liter bucket, leaving 2.5 in the big one. Top up the small one with 0.5L (total usage 5.5L), then do the glass half full trick to the big one, leaving 4L in the big one and an unneeded 1.5L in the small one.[/hide]


Assuming that you can half-empty either container but not half-fill it:
[hideb]
Fill 3; half-empty into 5.
Fill 3; half-empty into 5 again.
Half-empty 5 down the drain and empty 3 into it.
[/hideb]
Title: Re: Water Buckets - eco version
Post by Grimbal on Apr 21st, 2016, 6:43am
Makes me think of another solution.

Put the 3-unit bucket inside the 5-unit one.  Fill the space between the two. That is 2 units.  Transfer that to the 3-unit bucket.  Repeat.  Transfer the 2 units back to the 5-unit bucket.

Okay, it depends on the volume of the bucket material.  But with standard metal buckets it shouldn't be too much.

Funny that the out-of-the-box solution is actually inside-of-the-other-bucket.
Title: Re: Water Buckets - eco version
Post by playful on Apr 21st, 2016, 1:04pm
@rmsgrey I'm sure your solution works, but the way it's currently worded, I'm not understanding it. Would you kindly flesh it out?

[hide]
>Fill 3; half-empty into 5.
At that stage, B5 holds 1.5, right?

>Fill 3; half-empty into 5 again.
At that stage, B5 holds 3, right? Not understanding why we did this twice.

At that stage I don't understand step 3 either.
[/hide]
Title: Re: Water Buckets - eco version
Post by Grimbal on Apr 21st, 2016, 2:53pm
The point is to save water.  You discard only 1/2 unit.
Title: Re: Water Buckets - eco version
Post by rmsgrey on Apr 22nd, 2016, 5:52am

on 04/21/16 at 13:04:01, playful wrote:
@rmsgrey I'm sure your solution works, but the way it's currently worded, I'm not understanding it. Would you kindly flesh it out?

[hide]
>Fill 3; half-empty into 5.
At that stage, B5 holds 1.5, right?

>Fill 3; half-empty into 5 again.
At that stage, B5 holds 3, right? Not understanding why we did this twice.

At that stage I don't understand step 3 either.
[/hide]


The goal is to have 3l in 5 and 1.5l in 3 - you could get there by filling 3, emptying into 5, filling 3, half-emptying 3 but that wastes 1.5l compared to half-emptying 3 into 5 twice
Title: Re: Water Buckets - eco version
Post by playful on Apr 22nd, 2016, 12:26pm
@rmsgrey
Wow finally got it. For some reason it hadn't clicked that "half-emptying the 5" containing 3 was yielding 2.5...
Thank you for explaining, you blew my mind. :)
Title: Re: Water Buckets - eco version
Post by JiNbOtAk on Apr 24th, 2016, 6:39pm

on 04/21/16 at 06:43:03, Grimbal wrote:
Makes me think of another solution.

Put the 3-unit bucket inside the 5-unit one.  Fill the space between the two. That is 2 units.  Transfer that to the 3-unit bucket.  Repeat.  Transfer the 2 units back to the 5-unit bucket.

Okay, it depends on the volume of the bucket material.  But with standard metal buckets it shouldn't be too much.

Funny that the out-of-the-box solution is actually inside-of-the-other-bucket.


Damn, this is good. I'm definitely going to use this solution for my future out-of-the-box solution example. Thanks Grimbal, you're da man!!


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