Every student could name at least one specific technique or problem solving method and all but one student named from two to six or seven and many students cited very specific examples of their uses. The most common method/technique was the pigeonhole principle and all students but one mentioned this. A summary what the students remembered is given below:

For one student the pigeonhole principlewas the only thing that was recalled but in relating it to a particular problem it did not seem relevant or applicable.

Two other students mentioned pigeonhole (and could cite a specific problem that used it) and one other method, for one student the extremal principle and the other then invariance principle but said they did not grasp this and so never used it.

Still another student recalled the pigeonhole principle, the extremal principle and described the process of doing an investigation, finding a pattern and then completing the problem by doing an induction.

One student remembered induction, coloring, the use of recurrence and the search for invariants and recalled using this in a problem about weights attached to the vertices of a cube, which is precisely how that problem was solved.

Another student's list included the pigeonhole principle, coloring, the extremal principle and the investigation/pattern/induction method and cited problems resulting in the Fibonacci sequence as ones in which this was used.

One student mentioned the pigeonhole, extremal and invariance principles.

Another student recalled using induction on Fibonacci problems, the use of the pigeonhole principle, the coloring technique as applied to problems about covering chessboards and also described the idea behind the extremal principle but could not recall a name of it.

One student recalled the use of investigation/pattern/induction as applied to the Fibonacci sequence problems as well as pigeonhole principle, coloring, the use of symmetry, the invariance principle and the extremal principle though no examples were given for these.

Yet another student could recall: pigeonhole, induction, invariants, coloring, extremal principle and gave specific applications of the pigeonhole principle (99 people at a party then at least two people know the same number of other people), investigation, invariants (the problem from the final involving seven coins) and the extremal principle.

Without giving examples another student cited pigeonhole principle, induction, coloring, the extremal prinicipal and also mentioned specific instances of using an alternative representation in a combinatorics problem as well as making use of ideas from elementary number theory.

Finally, one student gave examples of the use of the pigeonhole principle, the use of congruence from number theory, the search for invariants and the extremal principle.