Vector Cloning

I don't know if this is a hypothetical question or practical...

You didn't really say which buffer you have been using but a double digest with EcoRI and BamHI requires the EcoRI buffer. Also, BamHI needs BSA so make sure you are adding this into the digest. Otherwise, I'm not sure where your problem could be. Is your plasmid just linearizing or is there no digestion at all?

A BamH1/EcoR1 buffer was added.  The number of blue colonies from the ligation was 226. They would have derived from incomplete digestion reactions, since all doubly-digested plasmids are unable to be religated. No white colonies could be obtained as there was no insert in the ligation reaction (some students reported white colonies but these must have been false whites). The question is: How could you do this experiment hypotheticaly if you were given an insert bearing a gene that was back-to-front, that is the restriction ends on the insert were in reverse order to the vector - EcoR1/BamH1 vs BamH1/EcoR1?