4.6 The Cook Oil Sharing Puzzle

Cally, Katy, and Jasnah buy a bulk container of 24 litres of cooking oil. The problem is that they intend to divide it evenly into 8-litre amounts in three different containers. The other two containers are 13 litres and 11 litres. They have a small 5 litre container that can be used. Katy comes up with a solution, and they all agree that dividing the oil will require seven careful steps. Can you find Katy’s solution or find one that takes fewer steps?

[latex]\begin{array}{ccccccccrccccc} &\text{Action taken:}&&&&&&\text{Each}&\text{container}&\text{holds:}&&&& \\ \\ \text{Step 1.}&\underline{\phantom{000000000000000}}\hspace{0.25in}&A&=&\underline{\phantom{00}}&B&=&\underline{\phantom{00}}&C&=&\underline{\phantom{00}}&D&=&\underline{\phantom{00}} \\ \text{Step 2.}&\underline{\phantom{000000000000000}}\hspace{0.25in}&A&=&\underline{\phantom{00}}&B&=&\underline{\phantom{00}}&C&=&\underline{\phantom{00}}&D&=&\underline{\phantom{00}} \\ \text{Step 3.}&\underline{\phantom{000000000000000}}\hspace{0.25in}&A&=&\underline{\phantom{00}}&B&=&\underline{\phantom{00}}&C&=&\underline{\phantom{00}}&D&=&\underline{\phantom{00}} \\ \text{Step 4.}&\underline{\phantom{000000000000000}}\hspace{0.25in}&A&=&\underline{\phantom{00}}&B&=&\underline{\phantom{00}}&C&=&\underline{\phantom{00}}&D&=&\underline{\phantom{00}} \\ \text{Step 5.}&\underline{\phantom{000000000000000}}\hspace{0.25in}&A&=&\underline{\phantom{00}}&B&=&\underline{\phantom{00}}&C&=&\underline{\phantom{00}}&D&=&\underline{\phantom{00}} \\ \text{Step 6.}&\underline{\phantom{000000000000000}}\hspace{0.25in}&A&=&\underline{\phantom{00}}&B&=&\underline{\phantom{00}}&C&=&\underline{\phantom{00}}&D&=&\underline{\phantom{00}} \\ \text{Step 7.}&\underline{\phantom{000000000000000}}\hspace{0.25in}&A&=&\underline{\phantom{00}}&B&=&\underline{\phantom{00}}&C&=&\underline{\phantom{00}}&D&=&\underline{\phantom{00}} \\ \end{array}[/latex]

Answer Key 4.6