Question

Thomas has four jugs of different sizes.one holds 1.2 liters, one holds 1.3 liters, one holds 2.3 liters, and one holds 2.6. He has to fill a large berrel with exactly 5 liters of water. How can he use the jugs to pour this amount into the barrel? Find as many ways as possible.

Answer 1

Thomas can use the four jugs in the following ways to pour exactly 5 liters of water into the barrel:

1. Using the 1.2-liter and 2.3-liter jugs:

• Fill the 2.3-liter jug with water.

• Pour the water from the 2.3-liter jug into the 1.2-liter jug until it is full. This leaves 1.1 liters in the 2.3-liter jug.

• Pour the 1.2 liters from the 1.2-liter jug into the barrel.

• Fill the 1.2-liter jug with the remaining 1.1 liters from the 2.3-liter jug.

• Pour the 1.2 liters from the 1.2-liter jug into the barrel. This makes a total of 2.4 liters in the barrel.

• Fill the 2.6-liter jug with water.

• Pour the water from the 2.6-liter jug into the barrel until it is full. This adds another 2.6 liters to the barrel, making a total of 5 liters.
  
  2. Using the 1.2-liter and 2.6-liter jugs:
• Fill the 2.6-liter jug with water.
• Pour the water from the 2.6-liter jug into the 1.2-liter jug until it is full. This leaves 1.4 liters in the 2.6-liter jug.
• our the 1.2 liters from the 1.2-liter jug into the barrel.
• Fill the 1.2-liter jug with the remaining 1.4 liters from 2.6-liter jug.
• Pour the 1.2 liters from the 1.2-liter jug into the barrel. This makes a total of 2.4 liters in the barrel.
• Fill the 2.3-liter jug with water.
• Pour the water from the 2.3-liter jug into the barrel until it is full. This adds another 2.3 liters to the barrel, making a total of 5 liters.

3. Using the 1.3-liter and 2.3-liter jugs:

• Fill the 2.3-liter jug with water.
• Pour the water from the 2.3-liter jug into the 1.3-liter jug until it is full. This leaves 1 liter in the 2.3-liter jug.
• Pour the 1.3 liters from the 1.3-liter jug into the barrel.
• Fill the 1.3-liter jug with the remaining 1 liter from the 2.3-liter jug.
• Pour the 1.3 liters from the 1.3-liter jug into the barrel. This makes a total of 2.6 liters in the barrel.
• Fill the 2.6-liter jug with water.
• Pour the water from the 2.6-liter jug into the barrel until it is full. This adds another 2.4 liters to the barrel, making a total of 5 liters.

4. Using the 1.3-liter and 2.6-liter jugs:

• Fill the 2.6-liter jug with water.
• Pour the water from the 2.6-liter jug into the 1.3-liter jug until it is full. This leaves 1.3 liters in the 2.6-liter jug.
• Pour the 1.3 liters from the 1.3-liter jug into the barrel.
• Fill the 1.3-liter jug with the remaining 1.3 liters from the 2.6-liter jug.
• Pour the 1.3 liters from the 1.3-liter jug into the barrel. This makes