perplexus.info :: Weights and Scales : Water and Oil

Water and Oil (Posted on 2005-06-21)

The classic pouring problems deal with one liquid, this one deals with two, water and oil. Properties of the oil and water are as follows:
- Oil floats on water.
- The water and oil never mix.
- The oil and water are both clear and can not be visibly distingushed.
- When pouring, the oil will always pour out before the water will.
- If water is poured into a jug containing oil, the water will sink down to the bottom.
- If oil is poured into a jug containing water, the oil will float on the water.

There is a 60 cup jug filled with 30 cups of water and 30 cups of oil. You also have three empty jugs with capacities of 43 cups, 11 cups and 7 cups to use.

Your task is to separate the oil from the water by pouring from jug to jug.

Example:
If your first move is to pour from the 60 cup jug to the 43 cup jug, the 43 cup jug will contain all 30 cups of oil and 13 cups of water.

Submitted by Brian Smith

Rating: 3.0000 (4 votes)

Solution: (Hide)

The trick is to never let any water leave the 60 cup container it starts in.
To do this, we need to find a way to express 30 as a combination of 7s and 11s. There are two options: 30=7*9-11*3 and 30=11*4-7*2. The second option uses fewer 7s and 11s, so that one will be used.
A +11 signifies pouring from the 60c jug to the 11c jug and then from the 11c jug to the 43c jug. A -7 signifies pouring from the 43c jug to the 7c jug and then from the 7c jug to the 60c jug.
Arranging 30 as 11 +11 -7 -7 +11 +11 solves the problem, so the list of pourings is:
60c to 11c
11c to 43c
60c to 11c
11c to 43c
43c to 7c
7c to 60c
43c to 7c
7c to 60c
60c to 11c
11c to 43c
60c to 11c
11c to 43c
The 60c jug now contains the 30c water and the 43c jug now contains the 30c oil.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
my solution is different, i think	christopher	2005-11-05 12:42:15
Wow!	john	2005-06-27 21:46:47
???	Somebody	2005-06-23 09:41:17
No Subject	Okash Khuwajo	2005-06-22 15:52:16
re(2): Solution	brianjn	2005-06-22 07:54:16
re: Solution	anonymous user	2005-06-21 18:25:46
Solution	anonymous user	2005-06-21 18:20:33

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