Can you solve it? Think of a number

A new twist on the all time classic maths trick

UPDATE: the solution can now be read here.

Think of a number" tricks are such a puzzle staple that the BBC even named a kids show after them. (To readers under the age of 40, Think of a Number was hosted by Zoe Ball's dad Johnny, and to many Britons, this one included, it was an indelible cultural highlight of growing up in the late 1970s/early 1980s.)

The following puzzle is a brilliant version of a think of a number' type problem, which I had not seen until recently. The solution is wonderfully ingenious. If you don't crack it now, or at all (as it consumes your day, sorry), you will be rewarded when I reveal the answer at 5pm.