On the Lottery Problem: Tracing Stefan Mandel's Combinatorial Condensation

Stefan Mandel is said to have won the lottery 14 times. He never disclosed the recipe he called combinatorial condensation, which enabled him to hit the Romanian lottery jackpot in the early phase of his betting career. Combinatorial condensation is frequently mixed up with another strategy known as buying the pot, which Stefan Mandel was pursuing later on. On occasion, he dropped a few hints on combinatorial condensation. The hints are applied in this work to narrow down and assess his initial recipe. The underlying theory resembles what a weekend mathematician, as he once referred to himself, may have encountered in the 1960s. The cardinality of the (15, 6, 6, 5) and (49, 6, 6, 5) lottery schemes shows that Stefan Mandel probably wasn't aware of lottery designs. First concepts on such topics had been available at that time, but coherent theories on combinatorial designs took off only in later decades. There is no absolute evidence beyond doubt, but the size of actual covering designs and the associated efforts allow the following hypothesis: Stefan Mandel most likely pioneered in constructing a (15, 6, 5) covering design many years before others published about it, which he applied in the Romanian lottery. Calculations indicate that he took considerable risks that his method might fail, because he limited himself to a subset of 15 numbers out of 49 numbers. The risks explain why he later changed his strategy from combinatorial condensation to buying the pot.