Soapy Smith gambling house. Legend has it that above the entrance of the stairway leading upstairs to the gambling games was a sign that read "caveat emptor", Latin for "let the buyer beware". Smith's younger brother, Bascomb Smith, joined the gang and operated a cigar store that was a front for dishonest poker games and other swindles, operating in one of the back rooms. Other operations included fraudulent lottery shops, a "sure-thing" stock exchange, fake watch and bogus diamond auctions, and the sale of stocks in nonexistent businesses. Because of bribes, some of the police officers patrolling the streets would not arrest
Problems in Latin squares a Latin square of order n. Estimate T(n). Describe how all Latin subsquares in multiplication tables of Moufang loops arise. A partial Latin square has "Blackburn property" if whenever the cells (i,j) and (k,l) are occupied by the same symbol, the opposite corners (i,l) and (k,j) are empty. What is the highest achievable density of filled cells in a partial Latin square with the Blackburn property? In particular, is there some constant c > 0 such that we can always fill at least c n cells? Let formula_1 be the number of Latin squares of order n. What is the