phyllo wrote:Really?

Is the number, the guru says, some secret code which allows them to skip days?

It's a "secret code" in that it's able to give extra information to the blue-eyed islanders under special key circumstances in the deductive process, even though at other points it just seems obvious to anyone.

And yes, the amount of islanders she refers to makes a difference that could skip days. Consider:

If she said she saw 100 blue eyed islanders, each blue would see 99 and deduce the 100th must be themselves. They all leave at the first opportunity. Each brown would already see 100 blues and think that no more information was added to what they could already see AND deduce.

If she said she saw 99 blues, and there were only 99 blues, they would leave by the same logic.

If she said she saw 99 blues, and there were 100 blues, each blue would be waiting for the 99 that they see to leave on the first day. They don't because they're all expecting others to leave and not themselves. They would each have deduced that there were either the 99 blues that they could see, or that there were 100 and each of them were the 100th after the 99 they each counted. Therefore since it's not the former, known and tested after the first day, they all leave on the 2nd.

If she said 98 and there were 100, the same logic continues in the way we should be used to by now. She can say any number and make it solvable, just as long as the number is less than or equal to the actual total amount of islanders with the eye colour mentioned by the Guru, and as long as the number is 1 or more. The same logic goes, it just makes the process either faster or slower.

The critical things to note are that the Guru's information conflicts with what is known just from looking at some point in the deductive process, and that the process MUST only consider what is definitely known for sure, and deductively exploring SOLELY within those confines in order to avoid risky assumptions like the alternative attempts mentioned so far, and that no information is taken out of context, such as the information known by 100 blues being used to deduce about what would happen if there were 1 blue knowing only what 1 blue would know. Once you get all these things, you should be home free to accepting the correct solution. Well done if you can, this is apparently very hard to do for some.