# 3
-- hints
i4 = 3

-- evens
(d5, f5) = 2 | 4 | 6 | 8

-- areasums
a1 + b1 = 8
a9 + b9 = 12

f1 + f2 = 10
d8 + d9 = 10

h1 + i1 = 8
h9 + i9 = 12

-- thermometer
a5 < b5 < c5
e3 < e4 < e5 < e6 < e7
g5 < h5 < i5

-- constrictions

--(d4 | b4) > d3 > (d4 | b4)
--(d4 | b4) > c3 > (d4 | b4)
--(d4 | b4) > b3 > (d4 | b4)

c2 | g2 > (d1, e1, f1) > c2 | g2
c8 | g8 > (d9, e9, f9) > c8 | g8
d4 | b4 > (d3, c3, b3) > d4 | b4
b6 | d6 > (b7, c7, d7) > b6 | d6
f4 | h4 > (h3, g3, f3) > f4 | h4
f6 | h6 > (f7, g7, h7) > f6 | h6

--(c2 > (d1, e1, f1) > g2) || (c2 < (d1, e1, f1) < g2)
--(c8 > (d9, e9, f9) > g8) || (c8 < (d9, e9, f9) < g8)
--(d4 > (d3, c3, b3) > b4) || (d4 < (d3, c3, b3) < b4)
--(b6 > (b7, c7, d7) > d6) || (b6 < (b7, c7, d7) < d6)
--(h4 > (h3, g3, f3) > f4) || (h4 < (h3, g3, f3) < f4)
--(f6 > (f7, g7, h7) > h6) || (f6 < (f7, g7, h7) < h6)
