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In this series, we will look at some fundamental puzzles to acquaint ourselves with these mind benders.
Total, we will look at the “pouring water puzzle” made famous by ‘Die Hard with a Vengeance’ where Bruce Willis and Samuel L. Jackson had to diffuse a bomb by placing a 4 gallon jug of water on a set of scales.
Here is the puzzle:
Question: You have a 3 and a 5 litre water container – each container has no markings except for that which gives us its total volume. We also have a running tap. We must use the containers and the tap in such a way that we measure out exactly 4 litres of water. How can this be done?
The question is not in the format of a standardised test but let’s worry only about the logic behind the puzzle. Thereafter, we can answer any question on it given in any format.
Let’s think about it: We have two containers only – one of 3 litre and the other of 5 litre capacity. The containers have absolutely no markings other than those which give us the total volumes i.e. the markings for 3 litre and 5 litre respectively. There is no other container. We do have a tap/faucet of water so basically, we have unlimited supply of water. Environmentalists may not like my saying this but it means we can throw out water when we need to and just refill again.
So think about it:
Let’s fill up the 5 litre container from the tap. So we are at (5, 0)
Now there is nothing we can do with it except transfer it to the 3 litre container (there is no other container and throwing off the water will bring us back to where we started). After we fill up the 3 litre container, we are left with 2 litre water in the 5 litre container.
This brings us to (2, 3)
Now, we gain nothing from transferring the 3 litre back to 5 litre so let’s throw out the 3 litre water from the container. We just threw out the 3 litre water from 3 litre container so we will gain nothing from refilling it with 3 litres of water now.
Now we are at (2, 0)
So next logical step is to transfer the 2 litre to the 3 litre container emptying out the 5 litre container. This means the 3 litre container has space for 1 litre more till it reaches its maximum volume mark.
This brings us to (0, 2)
Now fill up the 5 litre container and transfer 1 litre to the 3 litre container (which previously had 2 litre water). This means we are left with 4 litre water in the 5 litre container.
Now we are at (4, 3)
This is how we were able to separate out exactly 4 litres without any markings on the two containers. We hope you understand the logic. Let’s take another question to help us practice.
Question 2: We are given three bowls of 7, 4 and 3 litre capacity. Only the 7 litre bowl is full of water. Pouring the water the fewest number of times, separate out the 7 litre into 2, 2, and 3 litre (in the three bowls).
Solution: This question is a little different in that we don’t have unlimited supply of water. We have only 7 litres of water and we need to split it into 2, 2 and 3 litres. So neither can we throw away any water, nor add any water. We just need to work with what we have.
We are at (7, 0, 0) and we need to go to (2, 2, 3).
STEP 1: The first step would obviously be pouring water from 7 litres bowl to the 4 litres bowl. So now you will have 3 litres of water left in the 7 litre bowl. This gives us the natural next step of pouring from 4 litre bowl to the 3 litre bowl.
We are now at (3, 4, 0).
STEP 2: From the 4 litres bowl, pour water into the 3 litre bowl. So now we have 1 litre in the 4 litre bowl.
We are now at (3, 1, 3).
STEP 3: Empty out the 3 litre bowl, which is full, into the 7 litre bowl which now has total 6 litres. No other transfer makes sense. If we transfer 1 litre to the 7 litre bowl, we get the (4, 0, 3) split which gives us nothing new. We already have a 4 litre capacity bowl and a 3 litre capacity bowl.
This brings us to (6, 1, 0).
STEP 4: Shift the 1 litre water from the 4 litre bowl to the 3 litre bowl.
We are now at (6, 0, 1).
STEP 5: From the 7 litre bowl, shift 4 litres into the 4 litre bowl. We are left with 2 litres water in the 7 litre bowl. Again, no other transfer makes sense. Pouring 1 litre into some other bowl takes us back to a previous step.
So we are at (2, 4, 1).
STEP 6: Now, shift water from the 4 litre bowl to the 3 litre bowl to fill it up. 2 litres will be shifted, bringing us to (2, 2, 3). This is what we wanted.
We took a total of 6 steps.
At each step, the point is to look for what helps us advance forward. If our next step takes us back to a place at which we have already been, then we shouldn’t take it.
Keeping these pointers in mind, you should be able to solve most of these pouring water puzzles!
