The Four Marbles Puzzle

DIRECTIONS for questions 1 to 4: Answer the questions on the basis of the information given below.

Bhargav and Pranav played a game, in which Bhargav randomly picked four marbles from a bag containing a large number of marbles of each of four different colours – Blue, Red, Yellow and Grey – and arranged them in four positions labelled 1, 2, 3 and 4. Pranav knows that the bag has marbles of these four colours but is not aware of the exact colours of the marbles that Bhargav picked or the positions in which Bhargav placed the marbles.

In each attempt, Pranav had to guess the colours of the four marbles and positions in which they were placed. After every guess that Pranav makes, Bhargav provides a three-digit number, called Guess Accuracy Number (GAN), which provides the following information, for each guess that Pranav makes:

• The first digit (left-most digit) denotes the number of marbles that are of the correct colour and in the correct position.

• The second digit (middle digit) denotes the number of marbles that are of the correct colour but in the wrong position.

• The third digit (right-most digit) denotes the number of marbles that are neither of the correct colour nor in the correct position.

For example, if Pranav guessed the colours of the four marbles to be Grey, Red, Yellow and Grey in positions 1, 2, 3 and 4, respectively, then a GAN of 211 indicates that 2 marbles are of the correct colour and correct position, and 1 marble is of the correct colour but in the incorrect position and 1 marble is neither of the correct colour nor in the correct position.

The game ends when Pranav correctly guesses the colour and positions of all the four marbles, and it is known that Pranav was able to correctly guess the colour and positions of the four marbles in his seventh attempt.

The first table below provides the GAN for each attempt that Pranav made. The second table provides the colours that Pranav guessed for each position in each attempt, but not necessarily in the order of attempts.

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1. How many yellow marbles did Bhargav pick?

   
   

2. In the fifth attempt, what is the colour of the marble that Pranav guessed to be in the third position?

   
   

3. Hanu, a logician, did not know either the colours of the marbles that Bhargav picked or the positions in which they were placed, but he was aware of the attempts that Pranav made and the GAN of each attempt. What is the earliest attempt after which Hanu can be sure of the colours and positions of the four marbles that Bhargav picked?

   
   

4. In which of the attempt did Pranav guess yellow to have been in the first position?

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Solutions to the puzzle:

1. Zero

2. Grey

3. 2

4. 6

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We have uploaded the solution of this puzzle in the comments.