A hypercube of bits
This is the kind of thing mathematicians know about almost instinctively - but most ordinary folks don't. It's a 4-dimensional cube drawn in a very nice way, with each corner labeled by a string of 4 bits.
If you haven't ever thought about this stuff, try these puzzles!Puzzle 1:
The same thing happens when you start at any number and move west-northwest. For example, when you go from 0110 to 1110. What always happens to the number when you move this way?Puzzle 2:
What happens when you move east-northeast? For example, when you go from 0110 to 1110.Puzzle 3:
What happens when you move north-northwest? For example, when you go from 1001 to 1101.Puzzle 4:
What happens when you move north-northeast? For example, when you go from 1001 to 1011.Puzzle 5:
There are 8 bit strings on the outside of this picture. What happens when you go from one of these to the one directly opposite?Puzzle 6:
There are also 8 bit strings on the inside of this picture. What happens when you go from one of these to the one directly opposite?Puzzle 7:
How many pictures of cubes can you find in this picture? The cubes will be a bit slanted.
This picture is a tiny part of a huge subject called coding theory
, which about efficiently sending messages as strings of bits, while making it hard for one message to get mistaken for another when an error occurs.http://en.wikipedia.org/wiki/Coding_theory #geometry