Dice, airplane, sequences, and a card game (start w/ computer explorations).

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Grade Vs Difficulty:
  EasyModerateChallengingPerplexing
1-2
3-4
5-6
7-8
9-10
11-12
13-14

Several challenging discrete math problems that invited computer explorations
to generate insight, make conjectures, and suggest proof strategies.

Circle-tested at the ASU Tempe Math Circle. http://math.la.asu.edu/~mathcircle/
The students used the freeware SAGE.