Patterns in Pascal's Triangle - with a Twist - How about the Patterns?

Kathleen M. Shannon and Michael J. Bardzell


Faculty Notes The figures above show six hexagons, each created by pasting together six identical copies of Pascal's Triangle mod some number. [There is no mathematical signficance in the pasting operation -- it is just a way to provide the appealing "kaleidoscopic" patterns, which may emphasize number patterns by repetition.] The mod numbers used fall into two different categories, three in one category, three in the other. Just by looking at the patterns, can you guess which sets of three hexagons go together? Want a hint?