That's what I thought at first, but how does the second person communicate to the third the color of the third's hat when he can only say the color of his own?
You can save about 50% by having everyone guess randomly.
You can save 50% or more if every even person agrees to call out the color of the hat in front of them. That way the person in front knows what color their hat is, and if the person behind also has the same colored hat then both will survive.
So how can 99 people be saved? The first wise man counts all the red hats he can see (Q) and then answers "blue" if the number is odd or "red" if the number is even. Each subsequent wise man keeps track of the number of red hats known to have been saved from behind (X), and counts the number of red hats in front (Y).
If Q was even, and if X&Y are either both even or are both odd, then the wise man would answer blue. Otherwise the wise man would answer red.
If Q was odd, and if X&Y are either both even or are both odd, then the wise man would answer red. Otherwise the wise man would answer blue.
1) Bertie is the mole (he would be the only one lying in this instance)
2) If there were two moles... It would be Cedric and Albert, because Bertie would be the only one telling the truth.
Correct!
Bertie is the mole. Both Albert and Cedric are telling the truth. Hence, when Albert said, "Bertie is a mole," he was telling the truth, and giving you the correct answer. When Bertie said, "Cedric is a mole," he was lying, as he himself is a lying mole. When Cedric responded, "Bertie is lying," he was telling the truth, and also affirming that Bertie was lying.
In the second case, if there were 2 moles, the identifications would be a direct inverse. Both Albert and Cedric would be moles, and Bertie would be telling the truth.
12PP for you.
Puzzle 019- Crossing the River- 15PP
A man needs to cross a river in a canoe. With him, he has a bag of grain, a chicken, and a fox. He can only carry one of the three at a time. If he leaves the grain and the chicken, the chicken will eat the grain. If he takes the grain, the fox will eat the chicken.
How does he successfully cross the river with his load?