## Carnival of Mathematics #33: Walking Randomly Saves The Day!

by

The 33rd Carnival of Mathematics is up at Walking Randomly! (who also hosted the 25th Carnival). This carnival was homeless until a couple days ago when Walking Randomly stepped up to the plate. For only having a few days to put it together, it contains an impressive number of posts. Many, but not all, have a technology bent.

The Carnival post also explains the following cool fact about the number 33: Most numbers below 1000 that are not of the form 9n±4 can be written as a sum of three signed cubes (meaning the cubes are positive or negative integers). As an aside, the way is not necessarily unique. For example, from this source:
12=73+103+(-11)3 and
12=97307053+(-9019406)3+(-5725013)3.

Up until 1999, the number 30 was the smallest positive integer that wasn’t of the form 9n±4 where there was no known way to write it as a sum of three signed cubes. But less than ten years ago a way was found (see this breakdown of numbers under 100), and now 33 is the smallest such number.