I have designed an icebreaker where people interact through the mechanism of comparators as in comparison based algorithms.
Each person receives a symbol and they may mutually compare symbols.
If they are dilligent enough they may sort themselves entirely through this information.
I have constructed a paper prototype which may be viewed and printed
here.
In it every person's symbol is printed in grey on their card and given any two cards, the relationship between them is in the lower right hand corner of one of them.
For instance if the person holding the 11 leaf clover sees a four leaf clover on their card with a less than card, this means that 11 leaf clovers are less than 4 leaf clovers in this abstract comparison.