### A new problem

OK, let's try a new problem this time: Project Euler #92. I happened across a YouTube video of a "live coding" session by Daniel Silverstone. It's worth your while. I admire the courage of someone willing to show such an unedited session, typos and all, and besides, the video shows just how expressive Haskell is.

So, having seen Mr. Silverstone's video, this is another case in which I can't pretend to having had all the insights myself. I will write the code, though; it's not copy and paste.

The problem has to do with a function that maps n to the sum of the squares of the digits of n expressed in base ten. I can't quite bring myself to use

Now, it can be shown that for non-zero n,

So, having seen Mr. Silverstone's video, this is another case in which I can't pretend to having had all the insights myself. I will write the code, though; it's not copy and paste.

The problem has to do with a function that maps n to the sum of the squares of the digits of n expressed in base ten. I can't quite bring myself to use

**show**, so...**sumSqDigits :: Int -> Int**

sumSqDigits n = sumSqDigits' n 0

where sumSqDigits' n !s

| n < 10 = n * n + s

| otherwise = let (q, r) = divMod n 10 in sumSqDigits' q (r * r + s)sumSqDigits n = sumSqDigits' n 0

where sumSqDigits' n !s

| n < 10 = n * n + s

| otherwise = let (q, r) = divMod n 10 in sumSqDigits' q (r * r + s)

Now, it can be shown that for non-zero n,

**iterate sumSqDigits n**will "end" with…