The Puzzle of the Four Cards and Four People: An Explanation

Today, we explore a puzzle that has puzzled many: there were 4 cards in a box and 4 people in the room. Each person took one card, but at the end there was still one card left in the box. How could this be possible? Let's dive into the logic behind this intriguing riddle.

Let's introduce the characters and the rules. There are four people: x1, x2, x3, and x4. Here are the rules they follow:

Rules of the Game

If xn has n as a non-composite number: Receive a card from the box.

If xn has n as a composite number: Take a card from its predecessor, n-1.

Let's break down the sequence step by step:

Step-by-Step Analysis

x1 takes a card from the box. Since 1 is neither a prime nor a composite number (it is special), according to the rule, x1 receives a card from the box. x2 has 2 as a non-composite number. Thus, x2 receives a card from the box. x3 has 3 as a non-composite number. Hence, x3 receives a card from the box. x4 has 4 as a composite number. Consequently, x4 takes a card from its predecessor, which is x3.

At the end of the sequence, the 4th card is the last card to be drawn, and since the 4th person (x4) took a card from x3, it does not mean that x4 took the last card. The box still has one card left, and this is because the x4 did not take a card from the box but from x3.

Why It Works

The puzzle hinges on the distinction between the card being taken from the box and from a person. The key insight here is that x4 taking a card from x3 does not imply that the card was taken out of the box at that moment. The box retains the card, and x4 simply redistributes it among the players.

Conclusion

The puzzle demonstrates the importance of logical reasoning and the need to carefully differentiate between actions within the rules. The result of the puzzle is a game of redistribution, and the box retains one card despite all the movements.

To sum up, it is possible for one card to be left in the box because the 4th person did not take a card from the box. Instead, x4 took a card that x3 had received from the box. The distribution process ensured that the box still holds one card.