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?

Guest Dec 18, 2019

#1**+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?**

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

heureka Dec 18, 2019

#2**+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**).

Gadfly Dec 18, 2019