VKontakte P-30 Задача 23 as of 01.06.17

   First notice that

   (x1^x2) v (x1 v x3)^(x1^y1)=0 is equivalent
   (x1^x2) v x1 v (x3^y1) this last one is equivalent
   x1 v ( x3^y1) due to absorption rule in Boolean algebra

   and so far converting each equation one by one.
  
  Converted system

  x1 v ( x3^y1)=0
  x2 v (x4^y2) =1
  x3 v (x5^y3) =0
  x4 v (x6^y4) =1
  x5 v (x7^y5) =0
  x6 v (x8^y6) =1

Now split system into two without any dependency between them

1.) In system 1 x1 =0,x3=0,x5=0  Number of solutions 2*2*3 = 12

x1 v ( x3^y1)=0
x3 v (x5^y3) =0
x5 v (x7^y5) =0

 
2) System 2 has 38 solutions.

 x2 v (x4^y2) =1
 x4 v (x6^y4) =1
 x6 v (x8^y6) =1

---------------------------
First column x4
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K4 = 3  ; K(X) for value  "1",  X=2,4,6
Z4 = 2  ; Z(X) for value  "0",  X=2,4,6
------------------------------
Second column x6
------------------------------
K6=  2*K4 + Z4 =8
Z6 = 2*K4 =6
---------------------------------
Third column x8
---------------------------------
K8=  2*K6 + Z6 = 22
Z8 = 2*K6 = 16


Resulting number of {x2,x4,x6,x8},{y2,y4,y6} corteges is 38

Finally, we get 12*38 = 456