# Brainstorming Puzzles Set 8 Guess the Hat Color | The Secret Mail

Logic is the art of making truth prevail

– Jean de la Bruyere

Algorithmic thinking is really important as it enhances your thinking skills and can be nurtured with practice. (Refer the previous tutorial to know more about Algorithmic Thinking and try the puzzles before moving on to the solutions.)

### Solutions for the previous problems

#### Puzzle 7.1 Solution –  A Knight, A Knave and A Spy

Correct Answer:  Vasu is the Knight, Ram is the Spy and Shyam is the Knave

Explanation: We know that the knight never lies, knave always lies and spy sometimes lies.
Assuming Vasu is the knight, Shyam should be the knave as knight never lies.
Again, his statement should be false as the knave always lies which is false in this case as well. Therefore, our assumption is true.
If we try for any other assumption, it would contradict the statement of the knight and hold true for the knave which is wrong.

#### Puzzle 7.2 Solution – A Knight, A Knave, A Spy and a Judge

Explanation: If Shyam’s answer to the question is “No”, the judge will not be able to draw a conclusion. On the other hand, if he answers “Yes”, the judge will be able to draw a conclusion that Shyam is, in fact, the spy.

Solving these puzzles is fun, isn’t it? So, wear your logic caps and get ready for your next brain workout:

### Quiz 8.1  – Guess the Hat Color

There are four people standing in a line such that the last person can see the hats worn by the three in the front, the second last can see the hats worn by the two in the front and so on.
There is a red hat, a black hat, a white hat, and the last hat is a duplicate of one of those colors.
Starting with the person standing at the end, all of them were asked their respective hat colors and all of them guessed correctly.
What could be the possible arrangement of those hats?

Solution Added – Solution of “Guess the Hat Color” puzzle

### Quiz 8.2 – The secret Mail

Ram wants to send a secret item to his friend Shyam via mail.
He knows that Ajay has access to his mail, but he doesn’t want Ajay to see that item. So, he puts the item in a box and locks that box but he can’t send the key of that lock.
How can he send that item to Shyam securely via mail so that Shyam is able to unlock the box and see the item without sending him the key?