Candis has an 11-liter can and a 5-liter. How can she measure out exactly 7 liters of water into a third unmarked container?
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Let's call the 11 litre can A
Let's call the 5 litre can B
Let's call the unmarked container C
So we're starting with A = 11, B = 5 C = 0 (assuming both cans are full and the third unmarked container is empty).
Step 1.
Empty B into C, this gives us A = 11 B = 0 C = 5
Step 2.
Empty A into B, this gives us A = 6 B = 5 C = 5
Step 3.
Empty B into C
This gives us A = 6 B = 0 C = 10
Step 4.
Empty A into B
This gives us A = 1 B = 5 C = 10
Step 5.
Empty B into C
This gives us A = 1 B = 0 C = 15
Step 6.
Empty A into B
This gives us A = 0 B = 1 C = 15
Step 7.
Empty C into A
This gives us A = 11 B = 1 C = 4
Step 8.
Throw away contents of C so that it is lost.
This gives us A = 11 B = 1 C = 0
Step 9
Empty contents of A and B into C
This gives us A = 0 B = 0 C = 12
Step 10.
Empty contents of C into B
This gives us A = 0 B = 5 C = 7
Candis now has 7 litres in teh unmarked container.
Hope this helps.
Let's call the 5 litre can B
Let's call the unmarked container C
So we're starting with A = 11, B = 5 C = 0 (assuming both cans are full and the third unmarked container is empty).
Step 1.
Empty B into C, this gives us A = 11 B = 0 C = 5
Step 2.
Empty A into B, this gives us A = 6 B = 5 C = 5
Step 3.
Empty B into C
This gives us A = 6 B = 0 C = 10
Step 4.
Empty A into B
This gives us A = 1 B = 5 C = 10
Step 5.
Empty B into C
This gives us A = 1 B = 0 C = 15
Step 6.
Empty A into B
This gives us A = 0 B = 1 C = 15
Step 7.
Empty C into A
This gives us A = 11 B = 1 C = 4
Step 8.
Throw away contents of C so that it is lost.
This gives us A = 11 B = 1 C = 0
Step 9
Empty contents of A and B into C
This gives us A = 0 B = 0 C = 12
Step 10.
Empty contents of C into B
This gives us A = 0 B = 5 C = 7
Candis now has 7 litres in teh unmarked container.
Hope this helps.