# Gomez LOGIC

Great News! You've been nominated to be advisor to the king. It's a great position meaning unbelievable wealth and prestige. Not to mention being a Royal Advisor is a great BABE MAGNET! Unfortunately, the king is one of THOSE kings. You know the kind. They select advisors based on the candidate's ability to discern hat color. If you get this job one of your first pieces of advice to the king will be to discard this silly system.

The king's advisory board is a four member panel and the king has decided that he wants a fifth advisor. That's the position you hope to fill. You know nothing about the rest of the advisors. They are cloaked in mystery. When you meet with the king he explains the rather complex rules to the 2001 Get A New Advisor Test:

"It's really quite simple" he says "you will be blindfolded and led into a room with the other four sages. One who tells the truth at all times, without fail. One who lies all the time without fail. One who alternates between truth and lies and One whose rules when he makes three statements are different from the other three sages. This final type of sage is also known as a mystic. "These sages are each wearing different coloured hats. The four colours are Red, blue, Green and Black. These hats also signify the power of each sage thusly" Here the king hands you a little leaflet with "Chain of Power" written on it.

Chain of power
Red = Most powerful
Blue = Second most powerful
Green = Third most powerful
Black = Least powerful.

"You have to deduce which sage tells the truth/lies etc., each sages position in the chain of power and the colour of each of the sages hats" the king continued "by listening to what each sage has to say. You can tell the sages apart because they all have very distinctive voices (convenient, eh?). "What you have to do is deduce from the sages statements the colours of each of their hats. If you answer correctly then you will be my next high-paid advisor. However, should you be wrong, you would be tossed into the fiery furnace. If you cheat you will be beaten, quartered, and then tossed into the furnace--so don't do that." "That's a bit violent," you say. "I'm having second thoughts about this"

"Oh, by the way," The king says "If you back out now you'll also get the furnace. I don't want any quitters in MY kingdom"

You are about to tell the king to take his hats and his test and stick them where the sun don't shine when you notice a parade of lovely ladies-in-waiting stroll slowly by. Hmm... OK...

"Bring it on!" you tell the king.

You are blindfolded and wheeled into the room where the sages are. The sages are, according to the king, labeled, A, B, C & D and you know that they will speak in that order.

Sage A says

(1) B is a mystic
(2) D's second statement is false

Sage B says

(1) Only one of C's statements is true
(2) The lying sage is two places higher in the 'chain of power' than the truth telling sage

Sage C says

(1) A does nothing but lie.
(2) D alternates consistently between truth and lies and he is not a mystic.

Sage D says

(1) A always tells the truth
(2) C is higher in the 'chain of power' than A

When they finish you think. For a very..long..time. You have to be right or else face certain death. It's all down to you now, can you figure out which sage tells the truth, which sage lies, which sage alternates evenly and which sage is the mystic? Can you tell their position in the chain of power and, most importantly, can you deduce the colour of their hats?