Math Puzzle: Three men walk into a room that is completely dark. On the table ar
ID: 3119527 • Letter: M
Question
Math Puzzle:
Three men walk into a room that is completely dark. On the table are 5 playing cards. 3 spades cards and 2 heart cards. Each man selects a card(blindly) and then affixes it to his head. After this each man is asked in sequence whether he knows the suit of the card that he blindly affixed to his head. If anyone guesses correctly, the men are set free. If anyone guesses incorrectly they all die. Given that the last man that will be asked is blind, is it possible for the men to guarantee their survival?
Answer question using mathematical supporting work and explanations.
Explanation / Answer
Given information:
There are 5 playing cards.
3 Spade Cards
2 Heart Cards
Now, it is given that the last man that will be "ASKED" is blind. Since the room is dark, it doesn't matter of all three are blind. Now, the important piece of information here is that the third man is being 'asked'. This suggests that the first two survived their turns. Therefore, they must have guessed the correct suits of their cards.
Now, if the first two men who survived their turns guessed the correct suits, following can be the possible scenarios:
(1) Both of the first two men had spades
(2) Both of the first two men had hearts
(3) Both had the different suit cards. That is, one of them had a spade and the other had a heart.
Now, if the first two men had the spades, then the third person may have one of the left spades or one of the two hearts. Therefore, we cannot guarantee his survival in this case.
If the first two men had hearts, then the third man can have one of the three spades. Therefore, if all of them initially knew that there were 3 spades and 2 hearts, then in this particular situation, we can Guarantee the survival of the third blind man. Because both the hearts are already taken and he can easily guess that the card affixed to his head is none other than a spade.
If the first two men had different cards, then the left options for the blind man are 1 heart and two spades. Therefore, we cannot guarantee that he would be able to guess the suit of the card affixed to his head in this case.
Hence, the only case in which they all can survive is, if the first two men chose hearts.