This is in continuation of A Cup Of Coffee.

You have a five cup mug, a three cup mug, a water supply, a sink with a drain, and a packet of instant coffee which when dissolved in one cup of water produces coffee of strength 100%.

The packet may be used at any time, but the entire contents of the packet must be dissolved into a single mug when it is used.

What integer values of c (from 1 to 25 inclusively) is possible if the task is to fix 4 cups of coffee at exactly c% strength? Prove that these are indeed the only possible values of c.

Add the coffee to a full 5 cup mug - makes 20%.
Pour off 3 cups of this into the other mug - leaves 2 cups of 20%
Fill the 5 cup mug back to the brim - 20% * 2/5 = 8%.

It just occurred to me that this is 5 cups not 4 cups...

Posted by Jer on 2012-03-07 09:12:08