We revisit the classical Lucky Ticket (LT) enumeration problem, in which an even-digit number is called lucky if the sum of the digits of its first half equals to that of its second half. We introduce two new subclasses — SuperLucky Tickets (SLTs), where all digits are distinct, and LuckyPrime Tickets (LPTs), where all digits are prime — and, study their combinatorial structure and enumerative complexity. Using generating functions and inclusion–exclusion techniques, we derive exact counts for both subclasses in the six-digit case: 6,480 SLTs and 364 LPTs. We also prove structural properties such as sum-symmetry and divisibility by 13, and characterize the worst-case gaps between consecutive SLTs and LPTs in numerical order. Complementing these exact results, we develop and evaluate a greedy algorithm that identifies the next SLT following a given ticket. This scheme also serves as an interactive classroom tool to teach heuristic search and constrained enumeration. Despite its simplicity, the algorithm succeeds in approximately one-third of the cases and illustrates the effectiveness of local heuristics for constrained enumeration. Finally, we provide simulations which quantify the empirical probability of encountering SLTs and LPTs within the next N-ticket window.
Citation
Singh & Dubickas "Constrained Enumeration of Lucky Tickets: Prime Digits, Uniqueness, and Greedy Heuristics"