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.

(In reply to re(2): Possible solution by broll)

Here is the sequence in question, leading to 2%, where you say it leads to 3%:

5Fill 5Pckt 5T 5Dump 3T 3Fill 3T 5T 3T 5Dump 3T 3Fill 3T 5T

In the below table the percentages are in parentheses.

        3mug    5mug
5Fill     0       5
5Pckt     0       5(20)
5T        3(20)   2(20)
5Dump     3(20)   0
3T        0       3(20)
3Fill     3       3(20)
3T        1       5(12)
5T        3(8)    3(12)
3T        1(8)    5(10.4)    
5Dump     1(8)    0
3T        0       1(8)
3Fill     3       1(8)
3T        0       4(2)
5T        3(2)    1(2)

Posted by Charlie on 2012-03-07 10:57:12