Nerd-gasms via the mind of softandonly.com
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Only possible answer I’ve been able to find for this one is pure guesswork on the author’s part, leading me to believe this one’s a true plot hole.

Didn’t That Sonic Screwdriver Get Destroyed And Rebuilt A Few Times?

Back in Smith And Jones for example? And The Eleventh Hour? It wasn’t just the casing that was different. I suppose the Doctor could have backed it up with the TARDIS on wifi. Stored the sums in the quantum cloud…