100 mathematicians are standing in a line, wearing a black or white hat. Each mathematician can ONLY see the color of the hats of the people in front of them. So the first person sees no hats, the last sees 99.

The mathematicians are allowed to talk to each other and decide upon a strategy, for a government rep is coming to cut off funding. Each person can only say “black” or “white.” If you correctly say what color hat you’re wearing, your funding is continued and you live. If you’re wrong, you lose your funding, and you may as well be dead.

How many mathematicians can you guarantee will keep their funding?

You are not allowed you use “tricks,” say a person delays one second before answering means A, two seconds means B, … You have to answer IMMEDIATELY what color hat you’re wearing.

Communicated by Gergely Harcos.

You should be able to do 50% easily. Can you do two-thirds? Three-fourths? 100%?