The Unstoppable Blob Riddle: Can You Save the Planet?

Imagine a scenario: a shooting star crashes to Earth, unleashing a monstrous blob. This isn't your average monster; it creeps, leaps, glides, and slides, proving utterly unstoppable. Weapons, fire, extreme temperatures – nothing can halt its rampage. It simply regrows, doubling in size every hour, threatening to consume the entire world. But there's a glimmer of hope.

The Sleeping Giant: A Moment of Opportunity

After each hour of relentless expansion, the blob enters a brief slumber, transforming into a flat triangle. This is your chance! Armed with a satellite-mounted nano-fission ray, you can cut the blob. However, when active, the blob heals instantaneously. The key lies in understanding the geometry of the cut.

The Acute Triangle Solution

Experimentation reveals a crucial discovery: cutting the sleeping blob into two triangles yields different results. The acute triangle portion, where all angles are less than 90 degrees, becomes inert, never to awaken. Conversely, the obtuse triangle, containing an angle greater than 90 degrees, springs back to life, continuing its destructive growth. Further tests confirm that only acute triangles remain dormant.

The Challenge: Seven Cuts to Save the World

With the blob resting in its triangular form, you have mere minutes to act. The nano-fission ray allows for clean, straight-line cuts between any two points on or inside the triangle. But there's a catch: you only have time for seven cuts before the satellite orbits away. Fail, and the blob consumes the planet. How can you divide the blob entirely into acute triangles using only seven cuts?

The Pizza Principle: A Geometric Savior

The challenge lies in avoiding obtuse and right angles. Each cut that reaches an edge seems destined to create either an acute and an obtuse angle or two right angles, leading to an endless cycle of re-growth. The solution, surprisingly, can be found in a common food: pizza.

From Triangle to Pentagon: Cornering the Blob

Consider squaring off a pizza, transforming it from a circle into an octagon. Cutting this octagon into slices creates eight acute triangles. This principle extends to other polygons, including heptagons, hexagons, and pentagons.

By cutting off the sharp corners of the blob's initial triangle, you create a pentagon. Just like the pizza, this pentagon can be divided into five acute triangles. This requires a total of seven cuts, rendering the entire blob inert and saving the planet!

The Aftermath: A World Saved, But What Now?

You've successfully neutralized the threat. The world is safe, but you're left with a collection of giant, virtually indestructible acute triangles. The next challenge? Figuring out what to do with them.

Tags: ["math", "puzzle", "geometry"]