Doctor Who, Sherlock, and Sheldon Cooper Crossover

Ever wondered what a fight between these three genious men would be like?

What if they somehow met and became instant friends, or rivals?

The world has come to a final end, and it won't be pretty. Sherlock Holmes and his smart deductions can't get him far this time.
The tenth Doctors tardis crash lands after a mysterious card that has one address on it, 221B Baker Street, appears right in front of him.
Sheldon Cooper has dreams that lead to his favorite train station with two of his favorite crime solving heroes sitting on a bench talking to eachother. A newspaper is held in one of their hands and the date reads July 24, a week from now.
The Doctors Sonic Screwdriver and tardis key are missing.
The newly found enemies took Sherlocks lover and best friend hostage.
And Sheldons comic books, games, most valuable possessions are stolen from thin air, along with every ounce of knowledge he has gained over the years.