Classic maths puzzle dealing with partitions cracked at last.

Curious patterns
Ramanujan noticed that whole numbers can be broken into sums of smaller numbers, called partitions. The number 4, for example, contains five partitions: 4, 3+1, 2+2, 1+1+2, and 1+1+1+1.

He further realised that curious patterns - called congruences - occurred for some numbers in that the number of partitions was divisible by 5, 7, and 11. For example, the number of partitions for any number ending in 4 or 9 is divisible by 5.

"But in some sense, no one understood why you could divide the partitions of 4 or 9 into five equal groups," says George Andrews, a mathematician at Pennsylvania State University in University Park, US. That changed in the 1940s, when physicist Freeman Dyson discovered a rule, called a "rank", explaining the congruences for 5 and 7. That set off a concerted search for a rule that covered 11 as well - a solution called the "crank" that Andrews helped deduce in the 1980s.

http://www.newscientist.com/article.ns?id=dn7180