Puzzle: Party Hats

 

 

 

A hacker hires 8 mathematicians to help him with credit card theft. They are a close-knit group of experts who all know that they are all very intelligent. As a test, he lines them up as indicated in the diagram, with 6 facing a brick wall from the North and 2 facing it from the South. Then he gives each mathematician a sealed bag containing a party hat that is either blue or green and a printout of this web page, with the hats erased from the diagram. In total, there are 4 blue hats and 4 green hats. They're instructed to close their eyes, open the bag, put on the hat, look at the printout, and refrain from looking behind them. Each mathematician can see all the hats in front of him. For example, mathematician #3 can see the hats of only #4, #5, and #6.

The hacker instructs them to attempt to determine their hat colour. The first mathematician to correctly announce his hat colour will be awarded a million-dollar bonus. Anyone who guesses an incorrect color, makes any other noise, touches another mathematician, moves out of the line, or looks at his hat or a hat behind him will be shot.

Question: Will someone win the bonus? If so, who? If not, which mathematician could guess with the best probability of being correct?