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Pouring water V.

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Pouring water V. - Back to the Water and Weighing Puzzles

Measure exactly 2 liters of water if you have:

1. 4 and 5-liter bowls

2. 4 and 3-liter bowls

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

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Pouring Water V. - solution

1st Fill the 5-litre bowl, overspill water from it to fill the 4-litre bowl, which you empty afterwards. Overspill the remaining 1 litre to the 4-litre bowl. Refill the 5-litre bowl and overspill water from it to fill the 4-litre bowl (where there is already 1 litre). Thus you are left with 2 litres in the 5-litre bowl.

2nd The same principle – this time from the other end. Fill the 3-litre bowl and overspill all of the water to the 4-litre bowl. Refill the 3-litre bowl and fill the 4-litre bowl to the top. And there you have 2 litres in the 3-litre bowl.

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You can solve both sets of buckets from both small-to-big and big-to-small. The green water is your solution, and the blue water is the alternate solution. My first solutions were the green solution for the 5/4 set and the blue solution for the 4/3 set. In both cases, your solution is faster, but I thought it interesting to note that you can do it either way.

post-215-1178668114_thumbgif

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Good picture - speaks more than a thousand words

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fill the 5 liter up and pour it in the 3 liter. The over flow is 2 liters.

There are many ways to solve this one.

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coolastro1016,

im new here but the problem clearly states two different problems so using the 5 and 3 liters is impossible since they arent on the same problem together

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Both cases have a 4 litre bucket. If you fill the bucket and then slowly empty it until the water is touch just touching one side of the top and is just barely touching all of the bottom, you have the bucket half filled and therefore 2 litres. Basically, picture cutting the bucket diagonally.

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Both cases have a 4 litre bucket. If you fill the bucket and then slowly empty it until the water is touch just touching one side of the top and is just barely touching all of the bottom, you have the bucket half filled and therefore 2 litres. Basically, picture cutting the bucket diagonally.

Excellent answer! Almost all buckets are symmetrical, so this will work.

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Both cases have a 4 litre bucket. If you fill the bucket and then slowly empty it until the water is touch just touching one side of the top and is just barely touching all of the bottom, you have the bucket half filled and therefore 2 litres. Basically, picture cutting the bucket diagonally.

Er, most buckets are tapered, aren't they?, and so this would not work at all. Or have I misunderstood your suggestion?

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Both cases have a 4 litre bucket. If you fill the bucket and then slowly empty it until the water is touch just touching one side of the top and is just barely touching all of the bottom, you have the bucket half filled and therefore 2 litres. Basically, picture cutting the bucket diagonally.

Er, most buckets are tapered, aren't they?, and so this would not work at all. Or have I misunderstood your suggestion?

You haven't misunderstood; you're just under the assumption that skbrown's solution won't work with a tapered bucket. It will, as long as it's symmetrical.

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Both cases have a 4 litre bucket. If you fill the bucket and then slowly empty it until the water is touch just touching one side of the top and is just barely touching all of the bottom, you have the bucket half filled and therefore 2 litres. Basically, picture cutting the bucket diagonally.

Er, most buckets are tapered, aren't they?, and so this would not work at all. Or have I misunderstood your suggestion?

You haven't misunderstood; you're just under the assumption that skbrown's solution won't work with a tapered bucket. It will, as long as it's symmetrical.

This is not true! If it were a cylinder it would work. If it's tapered, it will not. Consider the extreme example of a bucket tapered to a point - you get a cone. How do you know when to stop pouring? Besides, we have BOWLS not buckets, which suggests an entirely different shape to me. Symmetrical or not, this method does not work with standard bowl or bucket shapes.

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Scenario 1: 4 and 5 litre bowls....

Fill the 5[-litre bowl], pour 4 litres into the 4[-litre bowl]; 1 litre remains in the 5.

Empty the 4 and put the 1 litre into the 4.

Refill the 5, pour into the 4 until full. 2 litres remain in the 5.

Scenario 2: 4 and 3 litre bowls....

Fill the 4, pour 3 litres into the 3; 1 litre remains in the 4.

Empty the 3, pour the 1 litre into the 3.

Refill the 4, pour into the 3 until full. 2 litres remain in the 4.

So exactly the same method, basically, but if I abstracted it with variables for smaller and larger bowls, it would probably be less clear.

Somewhat fewer than 1000 words....

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The question is poorly worded. Among other things, it does not make clear that you only have each of the two differently sized bowls.

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Er, most buckets are tapered, aren't they?, and so this would not work at all. Or have I misunderstood your suggestion?

You haven't misunderstood; you're just under the assumption that skbrown's solution won't work with a tapered bucket. It will, as long as it's symmetrical.

This is not true! If it were a cylinder it would work. If it's tapered, it will not. Consider the extreme example of a bucket tapered to a point - you get a cone. How do you know when to stop pouring? Besides, we have BOWLS not buckets, which suggests an entirely different shape to me. Symmetrical or not, this method does not work with standard bowl or bucket shapes.

ok... maths says he's right... but i sure liked the answer... :D

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You can solve both sets of buckets from both small-to-big and big-to-small. The green water is your solution, and the blue water is the alternate solution. My first solutions were the green solution for the 5/4 set and the blue solution for the 4/3 set. In both cases, your solution is faster, but I thought it interesting to note that you can do it either way.

really nice solution by fosley :D

i got the solution but i appreciate more the alternate ones.

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fill the 5 liter up and pour it in the 3 liter. The over flow is 2 liters.

There are many ways to solve this one.

---------------------------------------------------------------------------------------------------------------------------------------------- jus stop when the 3 liter bowl filled

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4 & 5 capacity, resolve to 2

A=4 size

B=5 size

A - B

is

0 - 0

Fill B(+5)

0 - 5

Pour B(-4) in to A(+4)

4 - 1

Dump A(-4)

0 - 1

Pour B(-1) in to A(+1)

1 - 0

Fill B(+5)

1 - 5

Pour B(-3) in to A(+3)

4 - 2

Edited by firepumpguy
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3 & 4 capacity, resolve to 2

A=3 size

B=4 size

A - B

is

0 - 0

Fill B(+4)

0 - 4

Pour B(-3) in to A(+3)

3 - 1

Dump A(-3)

0 - 1

Pour B(-1) in to A(+1)

1 - 0

Fill B(+4)

1 - 4

Pour B(-2) in to A(+2)

3 - 2

Very interesting that the steps with sizes 3 & 4 are the same as those of sizes 4 & 5.

Edited by firepumpguy
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1. fill the 4, put in the 5, fill four put as much as u can in five leaveing 3litres in the 4 then empty the 5 and put it in the 3 litres from the 4 in the 5 then fill the 4 and pour into 5 leaving 2 in the 4

2.fill the 3 pour into 4 fill 3 pour into 4 leaving 2 in the 3

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