Hey guys I remembered one old puzzle and thought of putting it on my web site. This is how puzzle goes.
There are three guys sitting on stairs as shown in the above diagram. We have five caps three of blue color and 2 of yellow color. We shuffle these caps and place one -one cap on all three guys heads such a way that all three guys don’t know what color cap they are wearing. We hide remaining two caps so all three guys don’t know what are the colors of remaining caps. From the sitting arrangement it is assumed that the person who is on stair #1 can see the caps of #2 & #3. Similarly person sitting on #2 can see the cap of #3. But last person sitting on stairs #3 can’t see anyone’s cap. Just to reiterate no one can see their own cap color and there is no turning back to see the previous person’s cap. Now I go to person sitting on stairs #1 and ask which color cap are you wearing? He replies I don’t know. Then I go to person sitting on stairs #2 and repeat the same question. He replies I don’t know. At last I go to person sitting on stairs #3 and repeat the same question. He replies I know. He tells me the correct color of cap he is wearing. Now you have to find out what is the color of cap person on #3 is wearing and how did he come to this conclusion.
Above puzzle is pure logic and there is no tricks. Please submit your response. It is fun solving puzzlesJ.
Nice puzzle.
Person on stair no. 3 should say BLUE
Explanation is in the table below 🙂
K – KNOW
DK – DON’T KNOW
1st 2nd 3rd
BBB DK DK
BBY DK K
BYB DK DK
BYY K K
YBB DK DK
YBY DK K
YYB DK DK
Answer is Blue cap.
The solution goes as follows :
O stands for Orange Cap and B for Blue cap.
Let us assume that 1 can see one of the following combinations :
B B
B O
O B
O O
O O combination is ruled out as 1 would have answered if he would have seen o o combination as there are only 2 orange caps.
2 can see one of the following combinations :
O B
B O
B B
2 would have told about the color of the cap he is wearning if it was B O combination. He is in a dilemma only because of the existence of the following combinations
O B
B B
So, definitely 3 can say that he is wearning Blue cap.
Nice puzzle Ajay!
My answer is that Person # 3 is wearing a Blue cap.
Here is the reasoning
P#1 is not seeing two yellow caps as that would lead him to answer that he is wearing a blue cap. As he is confused about what he is wearing, it means he is seeing either 2 blue caps or a blue and a yellow cap.
Now, if P#2 is seeing a yellow cap, he knows that he is not wearing a yellow cap as that would make P#1 answer the color of his cap. And also, then P#2 can say that he is wearing a blue cap.
As P#2 is also confused about what he is wearing, it means he is seeing a blue cap on P#3.
P#3 analyzes all this and answers that he is wearing a blue cap.
Blue…