A paleobotanist is examining fossilized leaf samples from two distinct geological periods. Each sample is analyzed for vein patterns, and the patterns are either monocotyledonous (M) or dicotyledonous (D). How many 5-sample sequences can the paleobotanist create if each sequence must contain at least one pair of consecutive samples with the same type?

Sun, 03 May 2026 10:58:03 +0000

A paleobotanist is examining fossilized leaf samples from two distinct geological periods. Each sample reveals vein patterns categorized as monocotyledonous (M) or dicotyledonous (D). Recent interest in ancient plant life has grown, fueled by emerging techniques in fossil analysis and increasing curiosity about how plant evolution reflects climate and environment across millions of years. This context makes understanding vein pattern sequences not just academic—but a window into Earth’s deep botanical history. The lab focuses on constructing 5-sample sequences from only M and D classifications. This problem explores not only combinatorics but also the subtle patterns hidden within fossil data. Understanding these sequences helps scientists interpret environmental changes over geological time and offers insight into evolutionary adaptations. ### What Does It Mean to Have Consecutive Matches?
Each fossil sequence of five samples must contain at least one pair of adjacent samples showing the same plant type—either MM or DD in a row. This condition reflects a subtle but significant shift in pattern consistency rather than random repetition, which matters when analyzing structure and function in ancient flora. This constraint rules out sequences where every adjacent pair differs (like MDMD or DMDMD), narrowing the total possibilities while remaining aligned with the core scientific interest in pattern continuity.