Four Gallons in a Five Gallon Bucket.

Solution by The Fallible Fiend

Once again I don't know where I first heard of this problem.  It may
have been way back in the late seventies or early eighties in one of
James Fixx's books.  I don't remember.  It really doesn't seem to be
much of a problem.  I kinda think it's only good as a real quickie.
That's probably because it's become ingrained in my consciousness.

You are given two buckets.  One holds precisely 3 gallons and the other
holds precisely 5 gallons.  You are also given a reservoir of water, say
a hose attached to the house spigot.  Your mission is to fill the 5 gallon
bucket with precisely 4 gallons of water.

You probably cannot eyeball this and get it very close, and if you can't
then you can do the following to accomplish the task:

5G = The five gallon bucket.
3G = The three gallon bucket.
R  = The reservoir.

                 +---------+
                 |         |
                 +---------+
                 |         |
+---------+      +---------+
|         |      |         |	State 0.  Start with both buckets empty.
+---------+      +---------+
|         |      |         |
+---------+      +---------+
|         |      |         |
+---------+      +---------+


		    		Step 1. Fill the 5G from R.
                 +---------+
                 |xxxxxxxxx|
                 +---------+
                 |xxxxxxxxx|
+---------+      +---------+
|         |      |xxxxxxxxx|
+---------+      +---------+
|         |      |xxxxxxxxx|
+---------+      +---------+
|         |      |xxxxxxxxx|
+---------+      +---------+


                                Step 2.  Fill 3G from 5G.
                 +---------+
                 |         |
                 +---------+
                 |         |
+---------+      +---------+
|xxxxxxxxx|      |         |
+---------+      +---------+
|xxxxxxxxx|      |xxxxxxxxx|
+---------+      +---------+
|xxxxxxxxx|      |xxxxxxxxx|
+---------+      +---------+


                                Step 3.  Empty 3G.
                 +---------+
                 |         |
                 +---------+
                 |         |
+---------+      +---------+
|         |      |         |
+---------+      +---------+
|         |      |xxxxxxxxx|
+---------+      +---------+
|         |      |xxxxxxxxx|
+---------+      +---------+


                                Step 4.  Empty 5G into 3G.
                 +---------+
                 |         |
                 +---------+
                 |         |
+---------+      +---------+
|         |      |         |
+---------+      +---------+
|xxxxxxxxx|      |         |
+---------+      +---------+
|xxxxxxxxx|      |         |
+---------+      +---------+


                                Step 5.  Fill 5G from R.
                 +---------+
                 |xxxxxxxxx|
                 +---------+
                 |xxxxxxxxx|
+---------+      +---------+
|         |      |xxxxxxxxx|
+---------+      +---------+
|xxxxxxxxx|      |xxxxxxxxx|
+---------+      +---------+
|xxxxxxxxx|      |xxxxxxxxx|
+---------+      +---------+


                                Step 6.  Fill 3G from 5G.
                 +---------+
                 |         |
                 +---------+
                 |xxxxxxxxx|
+---------+      +---------+
|xxxxxxxxx|      |xxxxxxxxx|
+---------+      +---------+	Final State.  4G in the 5G bucket.
|xxxxxxxxx|      |xxxxxxxxx|
+---------+      +---------+
|xxxxxxxxx|      |xxxxxxxxx|
+---------+      +---------+


----------------------------
Note: There's at least one other solution, but the one I know takes
more steps than this.