perplexus.info :: Just Math : A dilution problem

A dilution problem (Posted on 2006-06-08)

You have a container containing 1 liter of pure blue liquid dye. The container is cunningly designed in such a way that up to one extra liter of liquid may be added, but only the excess over 1 liter may ever be poured out. (If the container were filled to 1.5 liters only .5 liter could be poured out.)

If you have only one liter of pure water, what is the minimum concentration you could dilute the dye in the container to?

Assume the dye is completely soluble and mixes instantaneously.

Submitted by Jer

Rating: 3.3333 (3 votes)

Solution: (Hide)

1/e or about 36.8%
Put the water in one drop at a time, then pour one drop of the mixture from the container. Each drop dilutes by 1/(1+1/x)). x drops dilutes it by (1/(1+1/x)))^x which approaches 1/e as x approaches infinity (by definition.)

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

Subject	Author	Date
Answer	K Sengupta	2008-02-26 06:09:09
re: solution	brianjn	2006-06-10 02:41:17
solution	Salil	2006-06-08 11:42:01
Short	e.g.	2006-06-08 11:03:04
re: Parcial Solution	Charlie	2006-06-08 10:47:00
Parcial Solution	Phil_Osopher	2006-06-08 10:32:44

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