-- example puzzle from https://www.janko.at/Raetsel/Kakuro/index.htm
-- fields must have a value 1 through 9. technically unnecessary
(a1, a2, a4, a5,
 b1, b2, b3, b4, b5,
 c2, c3, c4,
 d1, d2, d3, d4, d5,
 e1, e2, e4, e5) = 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

-- fields can only have a single value
~~ a1, a2, a4, a5,
   b1, b2, b3, b4, b5,
   c2, c3, c4
   d1, d2, d3, d4, d5
   e1, e2, e4, e5

-- no duplicate values in a sum
!! a1, a2
!! a4, a5
!! b1, b2, b3, b4, b5
!! c2, c3, c4
!! d1, d2, d3, d4, d5
!! e1, e2
!! e4, e5

!! a1, b1
!! d1, e1
!! a2, b2, c2, d2, e2
!! b3, c3, d3
!! a4, b4, c4, d4, e4
!! a5, b5
!! d5, e5

-- puzzle-specific sum hints
17 = a1 + a2
11 = a4 + a5
15 = b1 + b2 + b3 + b4 + b5
13 = c2 + c3 + c4
18 = d1 + d2 + d3 + d4 + d5
10 = e1 + e2
14 = e4 + e5

12 = a1 + b1
4  = d1 + e1
21 = a2 + b2 + c2 + d2 + e2
22 = b3 + c3 + d3
16 = a4 + b4 + c4 + d4 + e4
13 = a5 + b5
10 = d5 + e5
