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# help

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Farmer Jim has an 8 gallon bucket full with water. He has three empty buckets: 3 gallons, 5 gallons and 8 gallons. How can he get two volumes of water, 4 gallons each, using only the four buckets?

Dec 18, 2019

#1
+23809
+2

Farmer Jim has an 8 gallon bucket full with water. He has three empty buckets: 3 gallons, 5 gallons and 8 gallons.

How can he get two volumes of water, 4 gallons each, using only the four buckets?

$$\begin{array}{|l|c|c|c|c|} \hline \text{buckets } & 8\ \text{gallons }& 3\ \text{gallons }& 5\ \text{gallons }& 8\ \text{gallons } \\ \hline \text{Start} & 8 & 0& 0& 0 \\ & 5 & 3& 0& 0 \\ & 5 & 0& 3& 0 \\ & 2 & 3& 3& 0 \\ & 2 & 1& 5& 0 \\ & 2 & 0& 5& 1 \\ & 2 & 3& 2& 1 \\ & 4 & 3& 0& 1 \\ \text{End} & 4 & 0& 0& 4 \\ \hline \end{array}$$

Dec 18, 2019
#2
+118
+2

Arrange the buckets as follows:

Full 8-gallon bucket--5-gallon bucket---3-gallon bucket---empty 8-gallon bucket

This arrangement is just for ease of reference and involves no magic. The water content of the buckets at the start of the process can be denoted by 8--0--0--0 (Full with 8 gallons--empty--empty--empty). In 7 steps, if I am not dreaming, the first and last buckets will each contain 4 gallons of water; so the water content meter will  read 4--0--0--4.

Step 1: Fill the 5-gallon bucket with the water from the full 8-gallon bucket (meter reading 3--5--0--0).

Step 2: Fill the 3-gallon bucket with the water from the 5-gallon bucket (meter reading 3--2--3--0).

Step 3: Pour the remaining two gallons of water in the 5-gallon bucket into the empty 8-gallon bucket (meter reading 3--0--3--2).

step 4: Empty the water content of the 3-gallon bucket into the 5-gallon bucket (meter reading 3--3--0--2).

Step 5: Fill the 5-gallon bucket with the water from the leftmost 8-gallon bucket (meter reading 1--5--0--2).

Step 6: Fill the 3-gallon bucket from the water contents of the 5-gallon bucket (meter reading 1--2--3--2).

Last step: Empty the contents of the 3-gallon bucket into the leftmost 8-gallon bucket and the contents of the 5-gallon bucket into the rightmost 8-gallon bucket (meter reading 4--0--0--4).

Dec 18, 2019
#3
+118
+2

Well this is amazing ! While I was writing my solution down, laboring through my meter readings, heureka solved the problem with a neat table, and what do you know he/she arranged the buckets in exactly the same order as I did! There is definitely magic involved here.

Dec 18, 2019
#4
+106519
+1

Dec 18, 2019
#5
+23809
+1

Thank you, CPhill !

heureka  Dec 19, 2019