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.

The following are possible integer percentages of the strength of a mug of 4-cup coffee, with those following the line break as those percentages inclusive between 1 and 25:
1/1*(100) =                          100%
4/5*(100) =                           80%
3/4*(100) =                           75%
4/5*( 80) =                           64%
4/5*( 75) =                           60%
4/5*( 60) + 1/5*((1/3)*(60))          52%
4/5*( 60) =                           48%
_________________________________________
3/4*( 75) =                           25%
1/5*(100) or 4/5( 25)                 20%
4/5*( 20) =                           16%
1/4*( 60) or 3/4( 20)                 15%
1/4*( 52) =                           13%
1/5*( 60) or 4/5*( 15) or 1/4*( 48) = 12%
1/5*( 25) or 1/4*( 20) =               5%
1/5*( 20) or 1/4*( 16) =               4%
1/5*( 15) =                            3%
1/4*(  4) =                            1%

Edited on March 7, 2012, 2:08 pm

Posted by Dej Mar on 2012-03-07 05:48:53