Why is a steel ball-bearing repelled from a magnet towards a piece of unmagnetised steel? At the risk of sounding like one of the Insane Clown Posse, I was watching this video of the late Eric Laithwaite discussing magnetism: 
Eric Laithwaite, Circle of Magnetism (1968)
(the relevant portion is between 05:30 and 06:05)
Basically, Professor Laithwaite demonstrates that a piece of unmagnetised steel will attract a steel ball-bearing away from a magnet, where the magnetic field is weakened by placing a piece of cardboard between the magnet and the ball-bearing. This surprised me. The video states an intention to go on and explain the phenomenon, but doesn't actually do so (at least from what I could see.)
Does anyone have an explanation of what is going on here? 
Some additional background: Eric Laithwaite, whilst very entertaining, was prone to dabble in areas of science that weren't actually his field of expertise. E.g., he's famous for his videos demonstrating properties of gyroscopes in which he makes unfounded claims about their ability to produce energy and "anti-gravity" effects. I suspect this may be one of those times when he noticed a phenomenon that is interesting, but that may have a more mundane explanation than he (or indeed I) appreciate. 
 A: An unmagnetised object will feel an attraction due to the gradient of a magnetic field - not its strength. All that is needed then is a piece of unmagnetised material that causes the gradient to point away from the magnet - the field lines need to be closer together further from the magnet.
This diagram may help explain:

As you can see, the field lines are closer together near the face of the piece of iron - and that means the direction of the attractive force on the unmagnetized steel ball is towards the piece of iron.
In essence, the iron acts as a concentrator of the magnetic field lines - because the magnet's face is larger, the density of field lines is lower there.
A: The steel –becomes temporarily magnetized- in the magnetic field of the permanent magnet.  In fact the field density at the surface of the steel bar is actually higher than the field density at a short distance from the magnet, because steel has a very high magnetic permeability.  So the bearing isn’t being attracted to an non-magnetized steel rod; it’s being attracted by both the magnetized steel and the permanent magnet, and at a given distance between the two, the steel wins.  If the steel could be completely shielded from the magnetic field of the permanent magnet, then it wouldn’t get magnetized and the bearing wouldn’t be drawn to it.  By the way, the magnetic field isn't "weakened" by the cardboard (magnetic fields pass unimpeded through most materials) - he just needed to keep the bearing far enough away from the magnet for the field induced in the steel to gain the upper hand on the attraction.
