Changing binary digits with different numbers of simultaneous operations
<p>I’m a maths teacher and have been given the following task for pupils to do.
3 pupils are sitting down.  Can all be changed from sitting to standing?  The only allowed move is for 2 people to change state from sitting to standing simultaneously (or vice versa).  It turns out it is not possible and in fact the only configurations that can be achieved are 0 standing and 2 standing.
Now if there are 4 people sitting with the same allowed move, clearly all can be changed to standing.  Again 1 and 3 people standing is not possible.
If the definition of a move is changed to 3 people changing from sitting to standing simultaneously (or vice versa).   Then for 4 people - 1,2,3, and 4 people standing can be achieved.  The pattern can then be investigated for different moves and numbers of people.
Since this is all about binary changes it seems to me that there must be some practical implication for this bit of logic from the world of computer science.  If there is, perhaps someone could enlighten me and I can add this as an extra hook to the lesson.  Thanks in advance.</p>