# Brainstorming Puzzles Set 6 – The Mystery Lock | The Witty Prisoners with Black/White hats

Logic is the beginning of Wisdom, not the end.

– Leonard Nimoy

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 5.1 Solution – Correct The Labels

Explanation: Pick the bag which is labeled as having both white and black balls. Since every bag is wrongly labeled, it must either have only white or only black balls but not both.

Scenario 1: If we found a black ball, that means, it has both black balls. Now we are left with two bags; one labeled as having two white balls and the other one labeled as having two black balls. But since we found the bag with black balls; we know that one bag contains only white balls which can only be the bag labeled as having only black balls
since the other one is labeled as having only white balls and we know that all the labels are wrong. The last bag remaining must have both white and black balls.

Scenario 2: If we found a white ball, that means, it has both white balls. Now we are left with two bags; one labeled as having two white balls and other one labeled as having two black balls. But since we found the bag with white balls; we know that one bag contains only black balls which can only be the bag labeled as having only white balls
since the other one is labeled as having only black balls and we know that all the labels are wrong. The last bag remaining must have both white and black balls.

#### Puzzle 5.2 Solution – The Five Weights

Correct Answer: The Jeweler made 5 rings weighing 1, 2, 4, 8, 16 grams

Explanation: Any number can be represented in binary form, therefore writing all powers of 2 before the maximum value(31 in this case) is the answer i.e till 16.

And using a combination of these weights we can form any weight. For example, if the man comes back on 27th then the King will offer the rings of weights 16, 8, 2,1.

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

### Quiz 6.1  – The Mystery Lock

There is a combination lock which can be opened only with a single combination of all the three numbers. Can you crack the lock code with the help of the hints given?

Hint1 – 682: One number is correct and well placed.
Hint2 – 614: One number is correct but wrongly placed.
Hint3 – 206: Two numbers are correct but wrongly placed.
Hint4 – 738: Nothing is correct.
Hint5 – 870: One number is correct but wrongly placed.

Solution Added – Solution of the Mystery lock puzzle

### Quiz 6.2 – The Witty Prisoners

A king gives his 100 prisoners a chance to earn their freedom. He tells them that, he’ll place all the 100 prisoners in a straight line and put a cap on their heads.
A prisoner can see the caps of all the people standing ahead of him but is unaware about his/her cap and the prisoners standing behind.

He says that the cap will be either white or black and he’ll place it randomly. He also says that all the prisoners will be allowed to say one word; either white or black.
If they say, their color they’ll be freed otherwise they’ll be killed. If anyone says some other word (other than WHITE or BLACK), all will be killed. He gives them one night to prepare a strategy for the game.
What to do you think would be the best strategy so that maximum lives can be saved?

So now think about the possible strategy on how to save the maximum lives from the King and post your answer in the comments.

Solution Added – Solution of The Witty Prisoners puzzle

So start thinking and comment answer to the questions asked above and wait for the next post for the solutions.
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Keep Learning. Happy Learning 🙂