I'm going to tell you a story. For that story to make sense, I need to give you some background context.
I have some pretty smart friends. One of them is Peter Schmidt-Nielsen. Peter has an illustrious line of descent. His paternal grandfather was Knut Schmidt-Nielsen, regarded as one of the great animal physiologists of his time. His paternal grandmother was Bodil Schmidt-Nielsen, who became the first woman president of the American Physiological Society. Bodil's father was August Krogh, who won the 1920 Nobel Prize in Physiology "for the discovery of the mechanism of regulation of the capillaries in skeletal muscle", and later went on to found the company that would eventually become Novo Nordisk.
Peter himself is no slouch. He was homeschooled for most of his childhood. When it was time to go to university, he simultaneously applied to MIT's undergrad and grad programs, and was accepted to both. (He decided to go to undergrad.) He went on to do some startup stuff, then was an early employee at Redwood. While there, he broke Meow Hash for fun. (He's not a security guy.)
My point here is: Peter is very, very smart.
Ok, here's the story.
One day I was in a room with Peter and Drake Thomas. Peter was telling us a story about a puzzle he'd grown up with, but never solved. Peter's father also went to MIT. While there, he decided to come up with a new "cube" puzzle, finding traditional cube puzzles like the Soma Cube too easy. Knowing that people often struggled with chirality, he decided to start with the six chiral pentacube pairs, but that left four cube units to complete a four-sided cube. Thinking that four 13 pieces would make it too easy, he decided to fill out the remainder with two 1x1x2 pieces (i.e. dominos).
He then cut the puzzle out of wood and spent some time trying to solve it. Not having any success, he left it overnight in the grad student lounge, and came back to find it solved the next morning.
Drake, hearing this story, said something to the effect of, "I think I can probably solve this puzzle in my head."
Impossible, right? No way a human can do that in their head in any reasonable time frame?
If you want to play around with the puzzle yourself, I've put a widget into the collapsible section below.
Pentacube Puzzle
After that, I watched Drake lie down on a couch and stare into space for two hours. Then he went to sleep. He came back downstairs the next morning and stared into space for another hour. Then he took a piece of paper and pen and wrote this down (in a spoiler block, in case you want to avoid any hints):
We didn't have a copy of the puzzle handy to make extra-sure, so they 3d printed one out and confirmed that the solution was correct.
Here are a couple of the original puzzles from the 70s:
The distribution of what unassisted human brains can accomplish is extremely wide. Human brains are squishy meat sacks. Better things are possible. Alas.
I'm going to tell you a story. For that story to make sense, I need to give you some background context.
I have some pretty smart friends. One of them is Peter Schmidt-Nielsen. Peter has an illustrious line of descent. His paternal grandfather was Knut Schmidt-Nielsen, regarded as one of the great animal physiologists of his time. His paternal grandmother was Bodil Schmidt-Nielsen, who became the first woman president of the American Physiological Society. Bodil's father was August Krogh, who won the 1920 Nobel Prize in Physiology "for the discovery of the mechanism of regulation of the capillaries in skeletal muscle", and later went on to found the company that would eventually become Novo Nordisk.
Peter himself is no slouch. He was homeschooled for most of his childhood. When it was time to go to university, he simultaneously applied to MIT's undergrad and grad programs, and was accepted to both. (He decided to go to undergrad.) He went on to do some startup stuff, then was an early employee at Redwood. While there, he broke Meow Hash for fun. (He's not a security guy.)
My point here is: Peter is very, very smart.
Ok, here's the story.
One day I was in a room with Peter and Drake Thomas. Peter was telling us a story about a puzzle he'd grown up with, but never solved. Peter's father also went to MIT. While there, he decided to come up with a new "cube" puzzle, finding traditional cube puzzles like the Soma Cube too easy. Knowing that people often struggled with chirality, he decided to start with the six chiral pentacube pairs, but that left four cube units to complete a four-sided cube. Thinking that four 13 pieces would make it too easy, he decided to fill out the remainder with two 1x1x2 pieces (i.e. dominos).
The six chiral pentacube pairs. Source: https://sicherman.net/c5nomen/index.html
He then cut the puzzle out of wood and spent some time trying to solve it. Not having any success, he left it overnight in the grad student lounge, and came back to find it solved the next morning.
Drake, hearing this story, said something to the effect of, "I think I can probably solve this puzzle in my head."
Impossible, right? No way a human can do that in their head in any reasonable time frame?
If you want to play around with the puzzle yourself, I've put a widget into the collapsible section below.
Pentacube Puzzle
After that, I watched Drake lie down on a couch and stare into space for two hours. Then he went to sleep. He came back downstairs the next morning and stared into space for another hour. Then he took a piece of paper and pen and wrote this down (in a spoiler block, in case you want to avoid any hints):
We didn't have a copy of the puzzle handy to make extra-sure, so they 3d printed one out and confirmed that the solution was correct.
Here are a couple of the original puzzles from the 70s:
The distribution of what unassisted human brains can accomplish is extremely wide. Human brains are squishy meat sacks. Better things are possible. Alas.