Given only an 11 liter jug and an 8-liter jug, each with no markings, find the method of using the two jugs to measure out exactly 1 liter of water while using the smallest amount of water. Argue clearly why you think that your procedure uses the smallest amount!
To measure out exactly 1 liter of water using an 11-liter jug and an 8-liter jug with no markings, you can follow these steps:
1. Start by filling the 8-liter jug completely.
2. Pour the water from the 8-liter jug into the 11-liter jug, which will leave 3 liters in the 8-liter jug.
3. Empty the 11-liter jug completely.
4. Pour the remaining 3 liters from the 8-liter jug into the empty 11-liter jug.
5. Refill the 8-liter jug completely once again.
6. Pour water from the 8-liter jug into the 11-liter jug until it is completely full. At this point, you will have poured 5 liters from the 8-liter jug into the 11-liter jug, and the 8-liter jug will have 3 liters remaining.
7. Now, the 11-liter jug contains exactly 5 liters of water. Empty the 11-liter jug.
8. Pour the remaining 3 liters from the 8-liter jug into the empty 11-liter jug.
9. Refill the 8-liter jug completely for the final time.
10. Pour water from the 8-liter jug into the 11-liter jug until it is completely full. This time, you will have poured 1 liter from the 8-liter jug into the 11-liter jug, and the 8-liter jug will have 7 liters remaining.
11. Now, the 11-liter jug contains exactly 1 liter of water.
To argue why this procedure uses the smallest amount of water, let's break down the steps. At each step, we make use of the 8-liter jug's full capacity, ensuring that we use the maximum amount of water it holds. We only make use of the 11-liter jug's full capacity once, in the final step when we transfer 1 liter of water. By utilizing the 8-liter jug to its maximum capacity twice and the 11-liter jug only once, we minimize water usage, making this the most efficient procedure.