Outsmarting a Magical Man: A Gold Coin Riddle

Imagine you're in a bind. To save your life, a magical being triples the gold in the king's treasury. The catch? You promise him your firstborn. Now, he's back to collect. Can you outsmart him?

The King's Demand and a Mysterious Helper

A few years ago, the king issued a daunting decree: triple the gold coins in his treasury, or face dire consequences. Just when hope seemed lost, a strange little man appeared, offering a magical solution. With a peculiar bag and a strange rhyme, he tripled the coins, saving your life. But this act of desperation came at a steep price – a promise of your firstborn child.

The Price of Magic

Years pass, and the little man returns, ready to claim what was promised. He reveals that his bag possesses a unique ability: it increases the number of gold coins placed inside it in a very special way. If any number of coins are placed in, more will come out. And if those are placed in the bag again, the total that comes out will be three times the original amount.

The Challenge

The little man presents a challenge. He takes 13 coins, places them in the bag, and then removes the contents. He declares that he has used the magic once, not twice, and demands you guess the number of coins in his hand. Guess correctly, and he'll show mercy.

Cracking the Code: How Many Coins?

The bag's magic operates like a mathematical function. If you put in 13 coins, then put the result back in, you get 39 coins. The challenge is to figure out how many coins are produced after the first use of the bag.

The Logic

Let's start with something easier. What happens to a single coin?
If you use the bag on a single coin twice, you end up with triple the amount; that’s three gold pieces.
Because the bag always increases the number of gold coins, the result of putting one coin in the bag must be between 1 and 3, so 2.
If 1 coin turns into 2, and 2 coins turn into 3, we can start to build a table.
Remember the rule: when you put more coins in, you get more coins out.
That means the numbers in every column must go in increasing order as well.
In other words, because 6 coins become 9, it’s not possible for 4 coins to become 10.
Nor could 4 become 5, since 3 becomes 6.
So 7 and 8 fill those blanks on the right of 4 and 5, which in turn gives the answer for two more blanks.
Knowing that the numbers go in increasing order in every column, the only choices for the remaining blanks are 19, 20, 22, and 23.

The Solution

Following this logic, we can deduce that 13 coins turn into 22 coins after the first use of the bag.

Victory Through Riddles

When the little man asks for your guess, you confidently answer, "22 coins." Astonished, he demands to know how you figured it out. You simply reply that you enjoy a good riddle.

This tale illustrates the power of problem-solving and logical deduction. By breaking down a complex problem into smaller, manageable steps, we can often find solutions that seem impossible at first glance. Just like outsmarting a magical man, tackling challenges with a clear and analytical mind can lead to unexpected victories.