No, no. Xiaoming's algorithm is unreasonable. To put it simply, what he said about 10 is not equivalent. For example, the case of 1 1 should actually include four cases: 1 100,101,1. This is equivalent to 000000 1, 00 10/0,001. According to him, 00 actually counts as four possibilities, while 1 1 counts as 1 possibilities. Of course not fair! A fair algorithm should list all four possibilities, 0000,0001,0010 ...1,11.There should be/kloc. Then look inside and see the probability ratio of winning the cake. That's fair.

By the way, the discussion mentioned at the beginning of this question is the cornerstone of probability theory. It is this discussion that gave birth to a new branch of mathematics-probability theory.