# Brainstorming Puzzles Set 5 – Correct the Labels | The Five Weights

The best way to predict the future is to create it.

– Abraham Lincoln

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 4.1 Solution – Joey’s Train

Explanation: Monica knows the hour but knows that Rachel doesn’t know, so it must be an hour with no unique minutes otherwise she won’t be so sure.
It can’t be 06 because that has 0643 and 43 is unique.
It can’t be 07 because 46 is unique.
So the hour must be either 08 or 09.

Once Rachel has worked this out if she knows the time it must be at minutes that aren’t shared between 08 and 09. So it must be 08:32, 09:17 or 09:50.

Monica now knows the exact time, so it must be 08:32.

#### Puzzle 4.2 Solution – Pirates And The Gold Coins

Correct Answer: The oldest pirate will propose a 98 : 0: 1 : 0: 1 split, in other words, the oldest pirate gets 98 coins, the middle pirate gets 1 coin and the youngest gets 1 coin.

Explanation: When the pirates vote, they won’t just be thinking about the current proposal, but all other outcomes down the line. Let us name the pirates (from oldest to youngest) be A, B, C, D and E. Lets work out the various cases:

Only 2 Pirates left: D splits the coins 100 : 0 (giving himself all the gold). His vote (50%) is enough to ensure the deal.

Only 3 Pirates left: C splits the coins 99 : 0: 1. E will accept this deal (getting just 1 coin) because he knows that if he rejects the deal there will be only two pirates left, and he gets nothing.

Only 4 Pirates left: B splits the coins 99 : 0: 1 : 0. By the same reasoning as before, D will support this deal. B would not waste a spare coin on C because C knows that if he rejects the proposal, he will pocket 99 coins once B is thrown overboard. B would also not give a coin to E because E knows that if he rejects the proposal, he will receive a coin from C in the next round anyway.

5 Pirates left: A splits the coins 98 : 0: 1 : 0: 1. By offering a gold coin to C (who would otherwise get nothing) he is assured of a deal.

Thus, the proposal of 98 : 0: 1 : 0: 1 split will be accepted by more than 50%.

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

### Quiz 5.1  – Correct The Labels

You have three bags, each containing two balls. One bag contains two black balls, another contains two white balls, and the last one contains one white and one black ball and you know that each bag is wrongly labeled.

How will you find out which bag is which by taking out only one ball?

Solution Added – Solution of Correct The Labels puzzle

### Quiz 5.2 – The Five Weights

A king asks a learned man to visit his palace, to which the learned man responds:
“I will come some day next month and you must give me the exact gold equal to the date on which I come.”

In preparation for the visit, the king demands that his jeweler make 5 gold rings instead of 1 to 31 grams. What are their weights?