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(b) This "system" sorts clients into three categories – either you are between steps 3 and 4 (working on drug tests), you are ready to do step 4, or you are out of the program. We need a black box that will sort clients into one of two categories: on to step four or out of program.

The main test for being out of the program is failing three tests. Otherwise you are still in until you pass three in a row. So, in English it might be "while you haven't failed thrice, keep testing until you get three in a row clean."

How do we combine these? To get our heads around it we need to NOT think about most of the system and focus only on these two features. Let's try this and see if it represents the system logic we want:

What does "All the Rest" have to accomplish? Drug tests. Count successes and failures. Warn on one failure, counseling on two. Reset success to zero after a failure. To think clearly about this, I want to remember that all I need to do is design logic that has a single entry point and a single exit point and that at the exit point we'll be ready to apply these tests about whether we are in the 3 passes in a row state, the 3 failures state, or the try again state.

Let's write out the logic in English:

1. Take a drug test.
2. If you pass, add one to the number of passed tests.
3. If you fail, set number of passed tests to zero (start over) and add one to the number of failed tests.
   1. If you have one failed test, get a warning
   2. If you have two failed tests, get counseling

I have an urge to follow this up with the next two tests, but remember I've got my "repeat while until" logic outside this black box. Let's see what this might look like.