Logic Puzzles

Naz_st

Assuming I was right with the above answer:

A king was looking for a knight for a dangerous quest. He has 3 equally brave, excellent and clever knights at his disposal, but he needs the smartest for this quest. So he blindfolds the three knights and brings them in to his audience chamber. He then places a hat on each of their heads and tells them: "I have placed either a white hat or a black hat on each of your heads. When your blindfolds are removed, I want you to raise your hand if you see a black hat, and lower your hand when you know the colour of your own hat". Now the wily king had placed a black hat on each knight’s head, and as soon as the blindfolds were removed, all 3 knights raised their hands. After a minute or so, one of the knights lowered his hand and said "My hat is black". How did he know? (And no, there are no mirrors etc in the room!)

twerg_85

Neonjack wrote: »

12 mins?
Crawly and Slowly cross - 10 mins
They throw the torch back to Speedy and Quickly
Speedy and quickly cross - 2 mins
Total 12

Mudskipper got the right answer, but I should have specified that torch had to be carried across.

twerg_85

Naz_st wrote: »

1 / 6 ?

Nope.

twerg_85

Naz_st wrote: »

Assuming I was right with the above answer:

A king was looking for a knight for a dangerous quest. He has 3 equally brave, excellent and clever knights at his disposal, but he needs the smartest for this quest. So he blindfolds the three knights and brings them in to his audience chamber. He then places a hat on each of their heads and tells them: "I have placed either a white hat or a black hat on each of your heads. When your blindfolds are removed, I want you to raise your hand if you see a black hat, and lower your hand when you know the colour of your own hat". Now the wily king had placed a black hat on each knight’s head, and as soon as the blindfolds were removed, all 3 knights raised their hands. After a minute or so, one of the knights lowered his hand and said "My hat is black". How did he know? (And no, there are no mirrors etc in the room!)

Actually, I think they should all have lowered their hand at the same time if they're equally clever ......
Each one knows that if they have a white hat, then their 2 opponents are each seeing one white and one black hat. Then your opponents would know that their hat is black so they would lower their hand. Since they didn't lower their hand, your hat is not white, i.e. black.

Naz_st

twerg_85 wrote: »

Nope.

Was a bit hasty there! A little trickier than I thought...

1 / 3 :

P(RR|R) = P(R|RR).P(RR) / P(R)
P(RR|R) = (1).(1/3) / (1/2) = 2/3

P(RB|R) = 1 - 2/3 = 1/3

x = (P(RR|R) * P(RB) * P(R)) + (P(RB|R) * P(RR) * P(R))

x = (2/3 * 1/2 * 1/2) + (1/3 * 1/2 * 1)
x = 2/12 + 1/6
x = 2/6 = 1/3

twerg_85

Naz_st wrote: »

Was a bit hasty there! A little trickier than I thought...

1 / 3 :

P(RR|R) = P(R|RR).P(RR) / P(R)
P(RR|R) = (1).(1/3) / (1/2) = 2/3

P(RB|R) = 1 - 2/3 = 1/3

x = (P(RR|R) * P(RB) * P(R)) + (P(RB|R) * P(RR) * P(R))

x = (2/3 * 1/2 * 1/2) + (1/3 * 1/2 * 1)
x = 2/12 + 1/6
x = 2/6 = 1/3

Spot on.