Join us as we explore A000136, the classic stamp-folding sequence. We trace how alternating folds—the shuffle pattern—drive a combinatorial explosion, helping explain why the counts jump from 1, 2, 6, 16, 50 and grow astronomically with more stamps. The discussion ties stamp folding to the caboosal puzzle and its restricted folding regimes (still NP-complete), shedding light on the deep structure behind this deceptively simple problem. We’ll also touch on a historical 1907 puzzle that foreshadowed these ideas and the role of computational origami in modern combinatorics.

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