The problem statement has to do with summing up digits in a large number if the 
digit matches the following digit, with wraparound.

My concept is to take the input as an array of single-digit numbers, compare 
this to itself rotated forward a digit. Wherever those match up, the following 
digit is a match. I can then copy to select the values that match and then 
simply sum them up. It works out like this:

   NB. First I want digits, so:
   a =. "."0 '<my big captcha string>'

   NB. Part 1: the idea is to line up the input against itself, rotated right 
one
   +/ a #~ a = 1 |. a

This worked, and then the twist in problem 2 turned out to be easy to 
compensate for: instead of hard-coding 1, calculate half the length of the 
array:

   NB. Part 2: rotate by half the length
   +/ a #~ a = (-: $ a) |. a

I did not even try to define these as functions, since I was sure I'd lose the 
plot trying to make them tacit and get frustrated.

-- 
Daniel Lyons




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