I'm a fan of Jeopardy, too..but I'm not in your geographic area so I can't advise of the repeat schedule. CBS is the network that caries it.
If you have On-Demand feature from your cable provider, you can request the replay of it. (Some people who are ambitious might call their cable provider and ask them about how to replay that episode. EPISODE #278 - Tuesday)
Otherwise, look on your cable listings for the time that this episode repeats..it might be 1 am or 2 am...for example. in your area it might be that episodes are now available (in some markets) during the daytime.
Also here's a link that might help you:
(Note on the right side it has a link for selection of what area you are located and your cable provider)