Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 253 games will be played during the tournament . what is the number of participants ?
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 253 n * ( n - 1 ) = 506 = 23 * 22 ( trial and error ) the answer is c ."
annotated_formula: divide(add(sqrt(add(multiply(multiply(253, const_2), const_4), const_1)), const_1), const_2)