Hello Carcul,

Carcul wrote:So, the purpose of this thread is to collect all logical solutions and other studies regarding Puzzle #77, and I invite here the others users of this forum to do that in this thread.

well, I will add my solution:

d6=6 or d5=6, k5=8, g5=5, c5=1, c12b3=456, a3=8, a456=6 > b6!=6

d6=6 or d5=6, (k2=4, c2=5 or k2=7, k7=2, f7=5 > f2!=5

k2=7 or k2=4, f2=9, d6=9, h6=2, g6=6, k4=7 > k7!=7 > k7=2, f7=5

k2=4 or k2=7, k4=6, g6=2, h6=9, f5=9, f2=4 > cd2!=4 > c2=5, b6=5, a8=5, b9=3 > ck1=46

h6=9 or h6=2, g6=6, k4=7, k2=4, f2=9, d6=9 > a6!=9

a2=9 or a2=1, a9=2, c4=2, c1=4, k2=4, k4=7, h4=9 > a4!=9

a4=2 or a4=6, k4=7, k2=4, f2=9, a2=1, a9=2 > a6!=2, ac4=2, h4!=2

c7=7, e7=8, h7=1 or c7=6, c8=7, c1=4, k1=6, k2=4, f2=9, f8=4, g8=1 > gh9!=1, ad9=12

h4=9, k4=7, k2=4, f2=9, a2=1, b7=1, g8=1, g9=4, eh79=78 contradiction > h4=7, k4=6, a6=6)

> g6!=6

d6=6 or d5=6, k5=8, g5=5, g6=2, h6=9 > d6!=9

d5=6, d6=4, (e6=3), k5=8, g5=5, g6=2, h6=9, (h4=7), (k4=6), a6=6, b6=5, c5=1, a5=3, f5=9, e4=1, f4=8, c12b3=456, a3=8, b1a2=19, cf2=45, k2=7, k7=2, a8=5, g3=6, b3=4, b4=9, a4=2, f2=4, f8=2, box3!=2 contradiction > d5!=6, d6=6

c5=6, (etc., c12=1

b4=4, b3=5, c4=2, e6=4, e1=3, e7=5, c7=2, k7=7, k2=4, c2=1, h1=1, 7!=1 > b4=1, b9=3, d5=1, f45=9

c4=4 or c4=2, a4=9, f5=9, e6=3, a6=5, b6=4, b3=5, c12=14, c78=57, a89=12, f1=3, h379=128, h1=5, f2=5, e14=48, e3=7, e7=5, c7=7, k7=2, f7=8, f4=4 > e4!=4, e4=8

f2=4 or f2=5, e16=35, e3=7, e9=1, a9=2, a4=9, f4=4, e6=3, e1=4 > d13e3f18!=4, b3=4, b6=5, a6=3, a5=9, a4=2, c4=4, a9=1, a8=5, f4=4, e6=3, f5=9, f1=3, f2=5, c2=1, c1=5, e1=4, k1=2, k7=7, k2=4, c7=2, c8=7, d1=8, h1=1, h7=8, h9=2, h3=5, g2=7, g3=8, e3=7, d3=2, d8=4, f8=2, g8=1, g9=4, e9=1, e7=5, f7=8, f7=?, contradiction >) c5!=6

a5=6, (k5=8, g5=5, g6=2, h6=9, h4=7, k4=6, c5=1, e4=1, d5=9, f5=3, e6=4, f4=8, e1=3, c12b3=456, a3=8, b1a2=19, ab6=35

b6=5 or b6=3, b9=1, a2=1, dgk2=478, c2=5 > b3!=5, c12=5

c4=4, c2=5 or c4=2, a4=9, a2=1, dgk2=478, c2=5 > c2=5

f2=4 or f2=9, b1=9, b4=4, d3=4 > d12f1!=4

k7=2 or k7=7, k2=4, k1=2, f2=9, f1=5, f7=2 > ch7!=2

k7=7 or k7=2, k1=4, c1=6, c7=7 > e7!=7

f7=5 or f7=2, k7=7, k2=4, f2=9, a2=1, b9=1, b6=3, b7=5 > e7!=5, e7=8, e9=7, e3=5, h7=1, h1=5

f1=2 or f1=9, f2=4, k2=7, d2=8, d1=2 > k1!=2, k1=4, k2=7, k7=2, f7=5, b7=6, c7=7, c8=2, c4=4, c1=6, b3=4, b4=9, a4=2, a8=5, a6=3, b6=5, a9=1, b9=3, a2=9, b1=1, g1=8, h3=2, h9=8, g3=6, d3=7, d2=8, d1=2, f1=9, f2=4, g2=1, d9=2, g9=4, g8=7, f8=4, d8=1, d19=2 contradiction >) a5!=6, gk5=6

d5=1, (c5=5, gk5=68, f45=9

b6=4 or e6=4, e4=8, f4=9, f5=3, a5=9 > b6!=9, be6=34

b6=4 or b6=3, a5=9, a6=2, e6=4, e4=8, f4=9, hk4=27, b9=1, a8=5, b7=6, b4=4 > c4!=4, b13!=4, de4=4

b1=9 or a2=9, a3=8, a4=6, a6=2, c4=1, b1=1 > b1=19

d2=9, de3=47 or d1=9, b1=1, c2=4, c1=6, b3=5, a3=8, > d3!=8, e3!=58

f2=8, a3=8 or f2=5, e7=5, a8=5 > a3!=5

h6=9, a6=2, g6=5, c124=146, c78=27, ab9=13, a8=5, b3=5, h1=5, f2=5, e7=5, box6!=1 contradiction > h6!=9, a6=9, h4=9, k4=7, a5=3, b6=4, e6=3, f5=9, f1=3, b1=9, d2=9, d1=2, k7=2, f27=58, f4=4, e4=8, e1=5, f2=8, a3=8, k2=4, de3=47, g2=7, c2=1, a2=5, b3=6, c1=4, b4=1, b9=3, b7=5, a89=12, c8=7, c7=6, c4=2, a4=6, f7=5, bf7=5 contradiction >) d5!=1

d5=9, (e4=1, f45=8

f6=4, b6=4 or f4=8, f5=3, ac5=15 > b6!=5

f1=3, f5=8, k5=6, g5=5, g6=2, h6=9, a6=5, b6=4, c5=1, c12b3=456, a3=8, a4=6, b4=9, a2=9, box4!=9 contradiction >) d5!=9, d5=8, k5=6, g5=5, g6=2, h6=9, c5=1, c12b3=456, a3=8, f45=9, a2b1=19, e4=1

f4=4, b6=4 or f4=9, a5=9, a2=1, b9=1, b6=3 > b6!=5, a6=5

f4=4 or f4=9, a5=9, a2=1, a8=2, c4=2 > c4!=4, c12=4, de3=4

d1=2 or d1=9, b4=9, f5=9, f1=3 > f1!=2, d13=2

f2=8 or f2=5, c2=4, k1=4, k7=2, f7=8 > f1!=8

a4=6, c4=2

cf28=5 x-wing > cf17!=5, f1=3, f5=9, a5=3, b6=4, b4=9, f4=4, e6=3, b1=1, a2=9, g2=1, d2=7, d1=9, d3=2, e3=4, b9=3, h7=1

e1=8 or e1=5, k12h1=248, g1=6 > g1!=8, which solves the remaining numbers.

Greetings, Maria