**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