I have two groups of questions. The first I would like to present to odd numbered respondents, the second to the even numbered respondents. How can I do this with LimeSurvey?

Hi,
you can use the group relevance equation field to set a condition on the last number of the respondant ID
Obviously, your survey must be activated

for 0, 2, 4 etc.
for 1, 3 , 5 etc

Note: {substr(SAVEDID, -1)} retrieve the last character of {SAVEDID}
.

Thanks Ben this will work fine for me.

Just out of interest, could I set up a counter of type integer in a hidden question at the top of the survey which I would be able access globally and do modular arithmetic on?

However I don't understand well your question... i think that you can achieve almost everything if you have an extensive look at all available EM functions .
For example I recommend you this old great post ...

SnowyEgret wrote: Thanks Ben this will work fine for me.

Just out of interest, could I set up a counter of type integer in a hidden question at the top of the survey which I would be able access globally and do modular arithmetic on?

If by counter you mean a counter for counting the current number of completed data sets, then this isn't possible because the Limesurvey placeholders can only refer to data of the current survey session.
Only the current data set ID ({SAVEDID}) can be used for that.