Transposing at Sight

A woodwind tutor in a youth orchestra told me this little anecdote a couple of years ago. I have no idea how true it is, but I would really like to think it actually happened!

Shortly after Jack Brymer was appointed as the principle clarinet of the LSO, the orchestra performed Borodin's Polovtsian Dances. The piece contains several rather tricky clarinet solos.  Jack played his part flawlessly, except for a slight slip on the first note of one of his solos.

After the concert, the conductor went up and talked to him. "That was some great playing, but what happened at the start?". "Sorry," Jack said, "I was on the wrong clarinet!". He had forgotten to switch onto his Bb for the solo, had played the first note a semitone flat on his A, and transposed the rest of the solo up a semitone to compensate. At sight.

My head hurts just transposing C parts onto Bb.