perplexus.info :: Weights and Scales : Lemonade

Lemonade (Posted on 2005-07-26)

You have 3 unmarked pitchers that hold 6 cups, 10 cups, and 15 cups. The 10 cup pitcher is filled with lemonade, but you have to dilute it so people at the party don't complain that it's too sour. Unfortunately, I have, in the name of logic, broken your only measuring cup.

How can you dilute the lemonade to 20 cups such that all of the lemonade is of equal concentration? You have a sink with unlimited water, but you can't waste any lemonade. Try using as few moves as possible.

Submitted by Tristan

Rating: 3.4000 (5 votes)

Solution: (Hide)

The best solution so far that strictly follows the rules has 9 moves, but you may find creative solutions with less moves in the comments. In the below chart of moves, P6, P10, and P15 represent the three pitchers. Each ratio is the number of cups of lemonade to the total number of cups.

P6 P10 P15 Move# 0:0 10:10 0:0 0 0:0 0:0 10:10 1 0:0 0:10 10:10 2 0:6 0:4 10:10 3 0:0 0:4 10:10 4 6:6 0:4 4:4 5 6:6 4:8 0:0 6 0:0 4:8 6:6 7 0:6 4:8 6:6 8 0:0 4:8 6:12 9
Thanks to jason aaron for finding this solution.

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

Subject	Author	Date
re: solution (I think it's the most efficient)	Why	2006-10-17 09:43:21
Solution (a truly simple one)	j	2006-02-19 18:21:11
re: solution (I think it's the most efficient)	thegnome54	2006-01-29 22:27:12
a 4 step solution	tanx	2005-10-17 20:40:38
answer	a guy	2005-09-26 21:07:00
re: Different from other solutions?	Tristan	2005-08-28 16:29:35
I think it is unique	jason aaron	2005-08-28 06:02:46
Different from other solutions?	jason aaron	2005-08-28 05:58:41
No Subject	Shelagh	2005-08-10 17:20:19
solution (I think it's the most efficient)	Libby	2005-08-08 01:51:42
re: Solution	Josh70679	2005-07-27 23:49:53
efficient, but is it cheating?	Josh70679	2005-07-27 23:33:28
re: Solution	Bob Smith	2005-07-26 17:26:07
Solution	Penny	2005-07-26 15:54:52
re: Solution, but not necessarily minimal	gail	2005-07-26 06:31:18
A less efficient solution	gail	2005-07-26 06:25:22
solution	mike	2005-07-26 02:29:07
Solution, but not necessarily minimal	Paul	2005-07-26 02:17:51

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