The guru does provide very indirect meta-information. Everyone's inaction cannot be taken as information on the first day, but inaction over time can. Consider

The guru does provide very indirect meta-information. Everyone's inaction cannot be taken as information on the first day, but inaction over time can. Consider the case with 100 brown and 1 blue person (+ guru). As soon as the guru speaks, the blue person knows their eye colour and leaves. Consider the case with 100 brown and 2 blue people. After the guru speaks, both of the blue people still don't know their own eye colour - the guru could have been thinking of the other one. So both blue people stay on the island on the first night. The other one staying on the island is information to the each of the blue people. Because the other blue one didn't leave on the first night, they must be also unsure - and therefore they must have blue eyes themselves. Both leave on second night. See also: http://img.spikedmath.com/comics/445-three-logicians-walk-into-a-bar.png http://img.spikedmath.com/comics/445-three-logicians-walk-in...