KöMaL 2026 K909

In the game of Six Bang', the players form a circle, and the first player says 1, and then each subsequent player says the next integer number, or a certain number of Bangs'. Bangs have to be said when at least one of the conditions below is satisfied, and the number of Bangs equals the number of conditions satisfied. I. Is a multiple of 6. II. Contains a digit that is 6. III. The sum of its digits is a multiple of 6. IV. The product of its digits is a multiple of 6. For single digit numbers both the sum and the product of the digits are equal to the number itself. a) Show two numbers, instead of which BangBang' should be said. b) A player had to say BangBangBang' instead of a number. Which condition was not satisfied? Find all possibilities.