A shooting star crashes on Earth, and a hideous blob emerges. It creeps and leaps, it glides and slides. It’s also unstoppable: weapons, fire, extreme temperatures… no matter what you throw at it, it just regrows and continues its rampage. Its expansion is breathtaking; it doubles in size every hour. But there’s one opportunity: after each hour, it goes to sleep, forming itself into a flat triangle and resting for a few minutes before it begins eating and growing again. Your only chance to save the planet involves a satellite-mounted nano-fission
ray that can cut through the blob. When the blog is active it heals itself within seconds. However, when you break the sleeping
blob into two triangles, you make a critical discovery. The acute triangle portion, with all angles less than 90 degrees,
is inert. It never “wakes up.” The obtuse triangle, which has an angle greater
than 90 degrees, wakes up as usual and keeps growing. Similar experiments show that all shapes
other than acute triangles, including right triangles,
will also wake up. For the next few minutes, the blob is sleeping in its
obtuse triangle form. You can make clean, straight-line cuts between any two points
on or inside the triangle. But you’ll only have time to make
7 cuts while the satellite is above you. By the time it completes
its orbit and returns, the blob will have consumed
the entire world, if even a single portion that
will wake up remains. How can you cut the blob entirely
into acute triangles and stop it from destroying the planet? Pause the video now
to figure out for yourself Answer in 3 Answer in 2 Answer in 1 While this seems doable at first, there’s a hidden difficulty when it comes
to avoiding obtuse and right angles. Every time you make a cut that
reaches an edge, it either makes an acute and
an obtuse angle, or two right angles. That makes it seems like you’re doomed
to keep creating obtuse angles. But as with so many of life’s problems, we can look to pizza for inspiration. Imagine squaring off the
outside of a pizza, so that instead of a circle,
it’s an octagon. When we cut it into slices, each of the eight triangles is acute. This works with larger polygons too. Importantly, it also works for some
polygons with fewer sides, including heptagons, hexagons,
and pentagons. That’s good news, because if you cut off the sharp corners
of the blob triangle, a pentagon is exactly what
you’ll be left with. And just like a pizza, you can cut the blob pentagon
into five acute triangles. That’s 7 cuts, and it renders the
blob completely inert. You’ve saved the day! Now you just need to figure out what to do with all of these giant, practically
indestructible triangles.
