The New Sudoku Players' Forum

[udosuk]

You are selling red wine in a huge barrel. You only have 2 perfectly cylindrical containers made of crystal-clear glass (unmarked at all), which are of identical height and thickness of material. One has a capacity of 3 litres and the other 5 litres. You don't have any other container or any measurement tool such as a ruler.

The first customer comes in with a bucket (unmarked of course), and wants 4 litres of red wine. Should be easy for you...

Next comes a couple with their own bottles (also unmarked). The husband wants 400ml while the wife only wants 250ml.

The 4th is an old man with another unmarked bucket, also asking for 4 litres. But he's very picky and doesn't like his wine being poured over and over... As a matter of fact he wants the wine to come straight from the barrel to his bucket with your cylindrical containers holding his wine at most once...

Could you satisfy all your customers' requests by giving them accurate amounts of wine?

(Notes: All the buckets/bottles the customers brought are of unknown capacities but should be large enough to contain what each of them wants. Your customers do not have any measurement tool as well. Your barrel is also unmarked. The floor of your shop is perfectly flat and level.)

[MCC]

Like you say, customer No.1 order is easy:

Fill the 5 litre container - fill the 3 litre container from the 5 litre container leaving 2 litres in the 5 litre container - empty this 2 litres into the bucket.

Repeat above for another 2 litres, empty into bucket, giving 4 litres in the bucket.


At the moment I don't think the couple wanting 400ml and 250ml litres of wine can be done without estimating amounts.
The lowest, accurate amount is 1 litre of wine.


The fourth customer I'll need to think about.


MCC

[Bigtone53]

If the two cylinders are the same height, then one must be broader than the other. If you put the 3L one inside the 5L one, the space in between is 2L. Fill the space with wine twice and the grumpy guy has his 4L.

Still thinking about the couple

[Bigtone53]

Gotcher! I won't spoil it for the others but I wondered why the floor was flat and level.

[ronk]

If you put the 3L one inside the 5L one, the space in between is 2L.

Wouldn't the wall thickness of the inner make that less than 2L?

[udosuk]

If the two cylinders are the same height, then one must be broader than the other. If you put the 3L one inside the 5L one, the space in between is 2L. Fill the space with wine twice and the grumpy guy has his 4L.

No no no... The internal space of the cylinders are 3L & 5L respectively, but if you put the 3L one inside the 5L one, it would probably occupy more than 3L (with the external body)... Therefore you'll get less than 2L... Try something else for the grumpy guy's 4L...

Since you've got a perfectly flat and level floor, you should be able to serve the couple's order accurately... For the picky old man it's a little tricky but with good skills and hand-eye coordination it could be done accrurately as well...

Technically speaking, MCC's method should be good enough for the old man's (4th customer) demand - you fill up 5L, pour 3L out, and the remaining 2L is held only once in the 5L cylinder... Let's think of a different method to serve the grumpy papa...

Most people would just do this for the 1st customer:

Code: Select all

0/3 + 5/5
3/3 + 2/5
0/3 + 2/5
2/3 + 0/5
2/3 + 5/5
3/3 + 4/5

[Bigtone53]

OK, I am happy to reconsider the grumpy old man but am satisfied on the couple (and interestingly, it seems that there being two of them is important). Do you want to hear the thoughts?

[udosuk]

OK, I am happy to reconsider the grumpy old man but am satisfied on the couple (and interestingly, it seems that there being two of them is important). Do you want to hear the thoughts?

From my own solutions, the couple's orders are served separately...
But I think you probably have a more innovative scheme...
Send me a PM and tell me all about it...

[JPF]

I know that it's not exactly the solution (I'm assuming that the 2 bottles are the same ).

Let's call A (5L) and B (3L) and X,Y the 2 bottles
L(A), L(B) the levels of wine in A and B, L(X) and L(Y) in X,Y.
The numbers of liters are given after the op.

Code: Select all

          A     B       X     Y
3->B      0     3
B->A      3     0
3->B      3     3
B->A      5     1
A->0      0     1
B->A      1     0
->B such that L(A)=L(B)
          1     0.6
B->X      1     0     0.6     0
A->Y   such that L(X)=L(Y)
         0.4    0     0.6     0.6
X->0
Y->0
A->X      0     0     0.4     0
->Y such that L(X)=L(Y)
          0     0     0.4     0.4
Y->A      0.4   0     0.4     0
A->B such that L(A)=L(B) 
          0.25  0.15
A->Y      0     0.15  0.4     0.25


JPF

[udosuk]

JPF, right concept (partially), wrong scheme...

You can NEVER make use of any container (buckets, bottles, etc) from customers when serving their orders, except to hold the final, accurate amount of products... It could be unhygienic, the shape could be irregular to prevent accurate measurement, and there is no guarantee the container is large enough to hold any temporary amount of products.

For example, when you want to pour 600ml of red wine to a bottle brought from a customer buying 400ml, it could well turn out that the bottle is only large enough to hold 435ml of liquid.

Failure to observe this rule will result in a formal warning. Repeated violations will result in serious reprehension.

[ronk]

Most people would just do this for the 1st customer:

0/3 + 5/5
3/3 + 2/5
0/3 + 2/5
2/3 + 0/5
2/3 + 5/5
3/3 + 4/5

But what to do with the 6 extra litres drawn from the barrel?

Having been exposed to bacteria in the air, it will again begin to ferment and turn to vinegar ... and returning the 6 litres to the barrel risks contaminating the entire barrel.

[Bigtone53]

For example, when you want to pour 600ml of red wine to a bottle brought from a customer buying 400ml, it could well turn out that the bottle is only large enough to hold 435ml of liquid.

They are a married couple so I am sure neither would mind the other's bottle being used to hold some of the 600 ml

[udosuk]

Doh... My bad... I've put too much limitations on the puzzle, that at the end the whole setup falls apart...

To make the whole thing work again, I guess we have to specify that the barrel is sitting in an isolated cellar (with the flat level floor) free of any bacteria, that the staff would come in with the 2 cylinders, measure the correct amount (with any excessive wine poured back into the barrel)...

Of course, if the shop owner is a generous bloke like me, he'd allow his staff to drink up any excessive wine exposed to the bacteria in the air... Just don't ask me how someone could drink 3 litres of red wine in one go...

[MCC]

...They are a married couple so I am sure neither would mind the other's bottle being used to hold some of the 600 ml

They were married but not to each other, their respective partners were paranoid and would measure any wine brought back.

The wine seller, having been in business some time, could estimate how much wine would be needed on any particular day, if any remained, it would do for his/her supper.

I can get down to 0.5 litres, you could estimate amounts if you're allowed to mark the containers


MCC

[udosuk]

They were married but not to each other, their respective partners were paranoid and would measure any wine brought back.

All irrelevant details... But even between spouses, sharing bottles of wine is sometimes considered unhygienic...

The wine seller, having been in business some time, could estimate how much wine would be needed on any particular day, if any remained, it would do for his/her supper.

No such estimation needed... Take a look at JPF's attempt... Make good use of your perfectly flat & level floor and the perfectly cylindrical shape of your cylinders...

I can get down to 0.5 litres, you could estimate amounts if you're allowed to mark the containers

No you're not allowed to mark any containers or estimate any amounts whatsoever... If you can get down to 0.5 litres accurately you should be not far from the correct solution...