Solving the Puzzle: Measuring Exactly 9 Liters Using a 10-Litre and a 7-Litre Bucket
Introduction to the Puzzle
Have you ever encountered a logical puzzle that seemed unsolvable at first glance, only to have an elegant solution revealed with a bit of thought? This is the classic problem of measuring exactly 9 liters using a 10-liter bucket and a 7-liter bucket. By following a series of steps, you can measure this specific volume with precision. Let's explore how to do it and delve into the logic behind this fascinating puzzle.
Step-by-Step Solution of the Puzzle
Method 1: The Correct Method
Fill the 7-liter bucket from the tap.
Pour the 7 liters from the 7-liter bucket into the 10-liter bucket.
Fill the 7-liter bucket again from the tap.
Pour from the 7-liter bucket into the 10-liter bucket until the 10-liter bucket is full. Since it already contains 7 liters, you can only add 3 more liters from the 7-liter bucket.
After pouring, you will have 4 liters left in the 7-liter bucket: 7 - 3 4.
Empty the 10-liter bucket completely.
Pour the 4 liters from the 7-liter bucket into the 10-liter bucket.
Fill the 7-liter bucket again from the tap.
Pour the 7 liters from the 7-liter bucket into the 10-liter bucket.
Now the 10-liter bucket contains 11 liters, but since it can only hold 10 liters, it will overflow. After the overflow, you will be left with exactly 9 liters in the 10-liter bucket.
In this method, each step is crucial to ensuring that the 9 liters are measured with precision. The key is to use the 7-liter bucket to measure out exactly 4 liters and then use these 4 liters as a reference to achieve the desired 9 liters.
Method 2: Simplified Approach with an Extra Container
Another approach involves the use of an extra container to help measure the 9 liters. Here are the steps:
Fill the 10-liter bucket with water from the tap.
Transfer 7 liters from the 10-liter bucket into the 7-liter bucket, leaving 3 liters in the 10-liter bucket.
Empty the 7-liter bucket.
Transfer the remaining 3 liters from the 10-liter bucket into the 7-liter bucket.
Refill the 10-liter bucket from the tap.
Use the 10-liter bucket to refill the 7-liter bucket, leaving 6 liters in the 10-liter bucket.
Empty the 7-liter bucket.
Transfer the 6 liters from the 10-liter bucket into the 7-liter bucket.
Refill the 10-liter bucket from the tap.
Use the 10-liter bucket once again to refill the 7-liter bucket, leaving exactly 9 liters in the 10-liter bucket.
In this method, the use of an extra container (which is at least 9 liters) helps simplify the process and ensures that the 9 liters are measured accurately. This approach involves direct transfers and refills, making it a bit more straightforward compared to the first method.
Conclusion
Much like solving any logic puzzle, the key to success in the 10-liter and 7-liter bucket puzzle lies in systematic thinking and precise execution. Whether you choose to use the first method or the second, both solutions demonstrate the power of logical reasoning and step-by-step problem solving. These puzzles not only challenge your mind but also enhance your skills in planning and strategic thinking. So, the next time you face a similar problem, remember the techniques we've explored and tackle it with confidence!