Problem: Measuring 4L using 3L and 5L Containers
This is a common puzzle often seen in brain teasers: “Let’s measure 4L using 3L and 5L containers!”
It was also featured in the famous action movie *Die Hard 3*. In the movie, there’s a scene where they have to measure water using containers at a park fountain, all while under the pressure of a time bomb. At that time, they needed 1 gallon, right? (1 gallon = 3.78L).
This is a brain teaser widely used not only in Japan but also around the world.
First, the standard methods: four different approaches
Here are three common ways to find the solution.
① Addition Method
1. Use the 3L container to pour 3L of water into the 5L container (the 5L container now holds 3L of water).
2. Again, fill the 3L container and pour water into the 5L container until it’s full (1L will be left in the 3L container).
3. Empty the 5L container. Then pour the remaining 1L of water from the 3L container into the 5L container.
4. Fill the 3L container again and add this water to the 5L container, which already has 1L. Now you have 4L.
② Subtraction Method
1. Fill the 5L container and pour water into the 3L container, leaving 2L in the 5L container.
2. Empty the 3L container, and then pour the remaining 2L from the 5L container into the 3L container (the 3L container now holds 2L of water).
3. Fill the 5L container again, and pour water into the 3L container until it’s full (1L of water will be added).
4. The 5L container now has 4L of water remaining.
③ Half Method
1. Depending on the shape of the containers, fill both the 5L and 3L containers with water.
2. Tilt the containers until you can see the bottom.
3. When both containers hold half of their capacity, combine the water from both into the 5L container to make 4L.
④ Modified Addition/Subtraction Method
1. Follow the addition method up to the point where the 3L container holds 1L of water.
2. Mark a line on the container at the 1L water level.
3. Now, you can use the 3L container to measure exactly 1L using the marking, and combine it to make 4L. This method can be used repeatedly.
You can also modify the subtraction method by marking the container.
Creative Solutions – Outside the Box?
By thinking freely, various solutions emerged.
⑤ Use MarketPlace/Mercari
Sell both the 3L and 5L containers and buy a 4L container.
That’s the Market-Place, Free market, and Mercari era for you.
⑥ Freezing Method
Freeze the combined 8L from both containers into ice blocks in a tray. Once it’s frozen solid, split it in half to get 4L.
A good idea.
⑦ Divide Total Water
Pour the 5L and 3L of water into a larger container (8L) and use a divider to split it in half.
That’s another option.
⑧ Bonus Method
Tell the person who posed the problem, “It’s 4L, but I’ll give you an extra 1L as a bonus! Smile!” and hand over 5L.
They reply, “What a waste to throw away water!” They have a point.
In this day and age, you could even hand them 3L and say, “I prepared 4L, but 1L got skimmed off in the middle.” *Bam!*
⑨ Evaporation Method
Pour 3L of water into the empty 5L container.
Then, use the 3L container to add 2L of water to the 5L container (now the 5L container holds 5L, and the 3L container holds 1L).
Leave them under the same conditions. When 3L evaporates, 1L will also evaporate from the 5L container, leaving 4L.
That’s a creative perspective. If both have the same surface area and are in the same environment, the amount of evaporation should be equal.
⑩ Scale Method
Subtract the weight of the 5L container on a scale, and you’ll be left with 4kg, which equals 4L.
Alternatively, you could drink 1L of water from the 5L container while standing on the scale, and when your weight increases by 1kg, 4L will be left.
⑪ Welding Method
Melt and reshape the 3L and 5L containers to make a 4L container.
That’s one option. After all, they’re not necessarily plastic.
⑫ Politician’s Method
Ask the person who posed the problem, “Does it really have to be 4L? Wouldn’t 5L be acceptable?”
Oh, that’s a reference to *that* person.
⑬ Faucet Control Method
Fix the faucet and measure how long it takes to fill the 3L container. Then calculate the time needed to pour 1L and create 4L.
This could count as a proper method, too.
⑭ Foolish Method (BAKA method)
A certain authority figure pours water into the 3L container and declares, “This is 4L, right?” Out of fear, many of their subordinates agree and say, “Yes, it is.”
This is the dark world of adult society. The origin of the word “fool.”
By the way, this story comes from ancient China, during the Qin dynasty (remember Emperor Qin Shi Huang?). The eunuch Zhao Gao brought a deer and said, “This is a horse,” and watched to see whether the officials would agree or not.
Conclusion
There are many ways to measure 4L using 3L and 5L containers. I’ve presented 14 different methods.
Not only standard methods, but approaches focusing on the containers themselves, questioning why 4L is necessary, freezing or evaporating the water, and more. It’s interesting to see so many different perspectives.
Once a single solution is presented, the thinking process tends to stop. However, when discussed in a group, various ideas keep emerging.
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