How does Brian solve the problem of not having a fire to cook the eggs in Hatchet?
Brian actually has a fire by the time he discovers the eggs, but is unable to cook them because he has no container in which to put them and hold them over the flames. He solves his problem by eating the eggs raw.
When Brian is trying to figure out what to do, he remembers his Uncle Carter, who "always put an egg in a glass of milk and drank it in the morning." The memory is not pleasant; Brian recalls "almost los(ing) everything he had ever eaten" as he watched "the runny part of the white (leave) the glass and (go) into his uncle's mouth and down the throat in a single gulp," but still, he is desperate. Brian bravely decides that "some natives in the world (eat) grasshoppers and ants and if they could do that he could get a raw egg down." Using his hatchet to poke a hole through the "surprisingly tough" shell of one of the eggs he has found, he closes his eyes and "suck(s) and squeeze(s) the egg at the same time and swallow(s) as fast as he (can)."
The egg, which is probably a turtle egg, has "a greasy, almost oily taste," but Brian forces himself to keep it down, and to his surprise, his stomach takes it and demands more to satisfy his gnawing hunger. Brian rapidly consumes five more raw eggs, even trying, to no avail, to see if the shell is edible, and saves the rest for later (Chapter 10).