Three Hats Puzzle

#212

In a game show, The Three Stooges; Moe, Larry and Curly entered the room, each with a hat on their head. There were two colors of hats: Black and Red, which were assigned to them randomly. Each person could see the hats of the two other people, but they couldn't see their own hats. Each person could either try to guess the color of their own hat or pass. All three do it simultaneously, so there was no way to base their guesses on the guesses of others. If nobody guesses incorrectly and at least one person guesses correctly, they all share a big prize. Otherwise they all lose.

Before the contest, The Three Stooges had a meeting during which they decided their strategy. What might be the best strategy?

  Difficulty Level - 3/5

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  Solution : 

  Will be updated in a day.
 

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Three Hats Puzzle - Hint

#212

In a game show, The Three Stooges; Moe, Larry and Curly entered the room, each with a hat on their head. There were two colors of hats: Black and Red, which were assigned to them randomly. Each person could see the hats of the two other people, but they couldn't see their own hats. Each person could either try to guess the color of their own hat or pass. All three do it simultaneously, so there was no way to base their guesses on the guesses of others. If nobody guesses incorrectly and at least one person guesses correctly, they all share a big prize. Otherwise they all lose.

Before the contest, The Three Stooges had a meeting during which they decided their strategy. What might be the best strategy?

  Difficulty Level - 3/5

  Update Your Answers : Click Here

  Hint : 

  Make the strategy by calculating the odds of winning by that strategy. 

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Coin Puzzle

#211

17 one rupee coins were distributed among 6 persons A to F. Each of them is a logician and each knows that at least 1 coin was received by each of them. However no one knew the identity of the person with maximum no. of coins. Then the following conversation took place :
A : "Mr. B, do u have more no. of coins than I have?"
B: "I don't know"
B: "Mr. C, do u have more no. of coins than I have?"
C: "I don't know."
Then the same question is posed by C to D and by D to E.
The replies given by D and E were the same as one given by C. After listening to this conversation, F claimed that he knew the no. of coins possessed by each of them.
What is the no. of coins with F?

  Difficulty Level - 5/5

  Update Your Answers : Click Here

  Solution : 

  Will be updated in a day.
 

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Coin Puzzle - Hint

#211

17 one rupee coins were distributed among 6 persons A to F. Each of them is a logician and each knows that at least 1 coin was received by each of them. However no one knew the identity of the person with maximum no. of coins. Then the following conversation took place :
A : "Mr. B, do u have more no. of coins than I have?"
B: "I don't know"
B: "Mr. C, do u have more no. of coins than I have?"
C: "I don't know."
Then the same question is posed by C to D and by D to E.
The replies given by D and E were the same as one given by C. After listening to this conversation, F claimed that he knew the no. of coins possessed by each of them.
What is the no. of coins with F?

  Difficulty Level - 5/5

  Update Your Answers : Click Here

  Hint : 

  > = <
  

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Mileage Puzzle

#179

A truck had travelled 40,000 kms and had used 5 tyres.
If all of the 5 tyres had been used equally in the journey, 
how many kms did each tyre sustain ??

  Difficulty Level - 3/5

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  Solution : 

   Each tyre sustained for 32000 kms each >>>
   >>> 40,000 * 4 = 1,60,000 >>>  1,60,000/5 >>> 32,000
  

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Mileage Puzzle - Hint

#179

A truck had travelled 40,000 kms and had used 5 tyres.
If all of the 5 tyres had been used equally in the journey, 
how many kms did each tyre sustain ??

  Difficulty Level - 3/5

  Update Your Answers : Click Here

  Hint : 

   Calculate the total distance.

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Dividing Horses Puzzle

#169

A rich old American had three sons. Before dying, he wrote in his will that his 17 Horses would be divided to his sons, as follows :- 
Eldest Son would get half of the Horses, 
Younger Son would get one-third of the Horses and
Youngest Son would get one-ninth of the Horses. 
After his death, the sons were unable to figure out how this can possibly be done. 
An old wise man without hesitation helped them in dividing the Horses properly. 
How did he do it?

  Difficulty Level - 3/5      

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  Solution : 

   9, 6, 2 
  >>>>  You have to take the LCM of the numbers (2,3,9) and have to find the nearest number to LCM(18) and then divide the horses.
                                                                   OR 
  You can say the old man temporarily added his horse to the 17, making a total of 18 horses.
1/2 = 9 , 1/3 = 6,  1/9 = 2 for a total of 17. 
He then took his horse back and ride away......

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Mathematical Reasoning Puzzle

#167

You are running a small business. To promote your brand, you decided to distribute Red, Black and Green Pens (having your brand name on them) among 100 persons. You have a budget of 100 dollars.
You decided not buy a single pen extra and also spending the exact $100 on buying pens. (Expecting printing cost nil)
The cost of different colored pens i.e Red, Black and Green Pens are $6, $3 ad $0.10 respectively.
So, what is the exact number of different colored pens will you buy ?

  Difficulty Level - 5/5

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  Solution : 

   Let "R", "B" and "G" be the number of Red, Black and Green Pens. We know two equations:
           R +   B +        G = 100                                       --- 1
        6R + 3B + 0.1G = 100                                --- 2
By multiplying the first equation by 6 and then 3 >>
        6R + 6B + 6G = 600
        3R + 3B + 3G = 300
Subtracting these two equations from the second, we can come up with two more equations:
                  3B = 500 - 5.9G
                  3R = 2.9G - 200 
Normally, two equations isn't enough to solve for three variables. 
But R,B and G are non-negative integers. 
So, if 3B ≥ 0, then 500 - 5.9G ≥ 0. This means G ≤ 84.75. 
Also, if 3R ≥ 0, then 2.9G - 200 ≥ 0. This means G ≥ 68.97.
i.e only two numbers can be possible which are 70 & 80.(as pens can't be fractional)
>>>> If G=80, then, R=10.67, and B=9.33. But R and B must be integers, so, it is not the solution.

>>>> If G=70, then, R=1, and B=29.

So, 1 Red Pen must be bought for $6.00, 29 Black Pens must be bought for $87.00, and 
70 Green Pens must be bought for $7.00.
  

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Mathematical Reasoning Puzzle - Hint

#167

You are running a small business. To promote your brand, you decided to distribute Red, Black and Green Pens (having your brand name on them) among 100 persons. You have a budget of 100 dollars.
You decided not buy a single pen extra and also spending the exact $100 on buying pens. (Expecting printing cost nil)
The cost of different colored pens i.e Red, Black and Green Pens are $6, $3 ad $0.10 respectively.
So, what is the exact number of different colored pens will you buy ?

  Difficulty Level - 5/5

  Update Your Answers : Click Here

  Hint : 

   Will be updated in a day.
  

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