What operation does this circuit perform?
Have another go at the numeric hint. The question told you they were binary values.

We normally write binary values left to right, same way as we do for decimal values. So the left hand column is most significant, so weight 4, and the right most column is least significant, weight 1.

You understand XOR gates, right? One way to look at them is 'they do the exclusive OR thang'. Another way to look at them is that they pass through a logic signal unchanged when the other input is 0, and invert it when the other input is 1. The logic operation described is identical, but sometimes it's easier to get what a circuit is doing using one or the other way.

If you look at the logic operation, a pattern emerges. 

The '1' output is always inverted. 

The '2' output is inverted when the '1' input is low.

The '4' output is inverted when both the '1' and '2' inputs are low.

That sequence is screaming out a pattern to me, like it's meant to do something sensible.

Anyhow, I'm not going to do your homework for you. You started in the right way, writing down all 8 sets of ones and zeroes. However if the answer didn't jump out at you, perhaps you picked a non-standard weighting. Try again with the weighting I suggest and have another look.