Suppose there were three events that could be done in any order. Let these events be A, B and C. There are a total of 6 possible ways the events can be performed.

However, this time, there is a restriction. B can only be performed after A. In other words, A must be performed before B can, and ACB is also accepted.

Your task is to find a general formula for X number of events, and Y number of restrictions.

None of the events is mentioned in more than one restriction.

The relationship between events and restrictions is easy! But it involves a new variable.

If you call 3 events term 1, you can call 4 events (and the corresponding restrictions) term 2, and so on and so on... 

You multiply the restrictions by 2, and if the term number is odd, you add on 1 after, to get the events.

2y+1 (if term is odd) = x

It's not that general, but general enough, I think. One question though - by restriction, do you mean strictly one event must come before/after another event, or do you mean things like one event must be first, one last, etc. Or is the whole problem much more complicated???  

Posted by Angela on 2005-02-15 19:10:59