Unraveling the Mystery of Numberland's Vampiric Crisis

In the vibrant realm of Numberland, a chilling mystery unfolds as prominent natural numbers are found drained of their essence. As Numberland’s best detective, you are called upon to solve this perplexing case. The city is under lockdown, but the attacks persist, described as a vampiric feeding frenzy. Can you decipher the patterns, identify the immune, and save Numberland from this mathematical menace?

The Crime Scene: A Detective's Analysis

Your investigation begins with a close examination of the victims. Some are completely drained, while others bear thin lines of slime, separating digits. This leads to the first crucial question:

• What is the significance of these slime-lines?
• Why are certain digits untouched?

Decoding the Prime Suspects

By analyzing the victims, a pattern emerges. The slime-lined numbers are prime numbers, divisible only by 1 and themselves. The untouched digits within these slimed numbers are also prime. For instance, when 71 is slimed, 7 is prime, while 1 is not.

• Prime Numbers: Divisible only by 1 and themselves.
• Non-Prime Numbers: Divisible by more than just 1 and themselves.

Consider the example of 2099, which is split into 20 and 99, both non-prime, allowing the attacker to drain them completely.

Identifying the Immune: A Race Against Time

The investigation takes a turn when you realize someone is kidnapping the numbers that can't be drained—the immune. These immune numbers hold the key to stopping the vampiric attacks.

The Characteristics of Immunity

Immune numbers possess unique qualities:

1. One-digit primes: 2, 3, 5, and 7.
2. Primes like 23, which can only be split into 2 and 3, both prime.

The Two-Digit Immune

To find the remaining immune, you focus on two-digit numbers composed of the digits 2, 3, 5, and 7. After eliminating numbers divisible by 2, 3, 5, and 11, you identify the two-digit immune: 23, 37, 53, and 73.

The Three-Digit Immune

Expanding the search to three-digit numbers, you look for combinations of the two-digit immune. This narrows the possibilities to 373, which is indeed prime and therefore immune.

The Vampire's Weakness: A Prophecy Revealed

Reaching the last immune number, 373, just in time, you learn of an ancient prophecy designating the immune as vampire slayers. These numbers, though pacifists, hold the power to defeat the vampire.

Confrontation and Resolution

Following the would-be kidnapper to a foreboding castle, you release the other kidnapped numbers and confront the vampire. Powerless before the slayers, the vampire is subdued, the lifeforce is returned to the victims, and Numberland is saved.

Conclusion: Numberland's Future

The mystery of Numberland's vampiric crisis is solved through keen observation, logical deduction, and a deep understanding of prime numbers. By identifying the immune and uncovering their prophetic role, you restore peace to Numberland, proving that even in a world of numbers, knowledge and courage are the greatest strengths.

Tags: mathematics, logic, puzzle