Tom Anderson wrote:
I want to cycle from London to Cambridge on saturday morning, take the
train to Norwich in the evening, take it back to Cambridge on sunday
morning, then come back to London on sunday evening. I'm thinking a single
big London - Norwich return is likely to be cheaper than a Cambridge -
Norwich return and a Cambridge - London single.

As you will discover, it is often not the case that one big ticket is
cheaper than a combination of tickets. In fact it's often cheaper to
'split' tickets in this way, especially if undertaking a day return
over a journey where day returns are not available (although I realise
that's not the case here).

A London-Norwich SOR is 66GBP.

London-Cambridge SOR is 35.80GBP
Cambridge-Norwich SOR is 20.90GBP

But you don't need a return from London-cambridge if you are cycling
one way, and there is no need for a SOR for Cambridge-Norwich; a Saver
will do fine.

A Cambridge-London SDS is 17.90GBP (CDS 17.50GBP), and a
Cambridge-Norwich SVR is only 16.70

So you only need to spend 17.50 + 16.70 = 34.20GBP (A saving of 31.80
off the London-Norwich SOR!)