. Ms. Shell has 2 opaque drums of capacity 8-liters and 5-liters, a resource of Oil, and a bit of brain. She uses these two drums to measure 1-liter, 2-liters, 3-liters, 4-liters, 6-liters and 7-liters to any customer. How can she do that? What steps shall she take for each order? Note that there is no marking of liters possible on the drums.
Answers
Answer:
yes, you can, mainly because 5 and 8 are relatively prime (and the required volumes are less than the combined volume of the drums)
Step-by-step explanation:
1. use the procedure for 6. below, empty [5], put 5 liter in [5] (then it's full) and you're left with 1 liter in [8].
2. fill [5], empty it in [8], fill [5] again, put 3 liter in [8] (then it's full) and you're left with 2 liter in [5].
3. fill [8], put 5 liter in [5] (then it's full) and you're left with 3 liter in [8].
4. use the procedure for 7. below, fill [5], put 1 liter in [8] (then it's full) and you're left with 4 liter in [5].
6. use the procedure for 3., empty [5], put the 3 liter from [8] in [5], fill [8], put 2 liter in [5] (then it's full) and you're left with 6 liter in [8].
7. use the procedure for 2., empty [8], put the 2 liter from [5] in [8], fill [5] and empty it in [8]. You're left with 7 liter in [8].