Natalia- When students write in about some school assignment, I usually rant about how dumb it is. Not this time. This is really interesting! It's so interesting that I can't resist the chance to do it, but you should not read further until you've thought about this as much as you can on your own.
Here's some thoughts.
0. (LeeH thought of this one, the best one. I completely missed it.) The force between the bars depends on how they point, in a different way for the magnet and the iron. Let's look at the simplest bar shape, a square. All four sides of the iron square are the same. The force between it and the magnet is the same (at some distance) regardless of which side faces the magnet. Now think of the square magnet. Two of its sides are pole faces and two aren't. The force depends on whether a pole face or a non-pole face is facing the iron.
For elongated bars, unfortunately even for the plain iron the force depends on whether the long direction or the short direction faces the magnet. So figuring out the quantitative difference in how the force depends on which way the iron points and which way the magnet points requires some calculation, which we're too lazy to do.
1. (not very practical, but would work in principle). Move the two bars back and forth near each other many times. The plain iron bar will magnetize and demagnetize repeatedly. Each time a little energy will dissipate inside it. It will heat up much more than the magnet will. Unfortunately, that may not be enough to feel, and it sounds as if using a fancy thermometer isn't allowed.
2. Break each bar in half. The two magnet halves will have strong forces between them which will change sign if you turn one piece 180°. The two iron halves won't have strong forces. A magnet half and an iron half will have fairly strong forces which will not change sign if you turn one by 180°. Unfortunately this is a somewhat destructive test.
3. Like 2, but you just break off a little piece and see what forces it feels from the big piece. This is a little less destructive.
4. (Suggested by Jon W.): You could repeatedly tap one of the bars. If it's the iron, nothing much will change. If it's the magnet, it will demagnetize a bit, reducing the force between them. If you get no effect after many taps, you could switch to trying the other just to make sure that you get some effect one way or the other. Warming (I assume you could at least use your hands) will help.
(published on 02/16/2011)