How many solutions are there for $x_1+x_2+x_3+x_4 = 49$?

Question

How many solutions are there for this equation $$x_1+x_2+x_3+x_4 = 49\,,$$ where $x_i,\;i= 1,2,3,4$ is a non negative integer such that:$$ 1\le x_1\le 8,\;3\le x_2\le 9,\;10\le x_3\le 20,\ 0\le x_4\,?$$

Answer 1

We have that $$ \eqalign{ & \left\{ \matrix{ 1 \le x_{\,1} \le 8 \hfill \cr 3 \le x_{\,2} \le 9 \hfill \cr 10 \le x_{\,3} \le 20 \hfill \cr 0 \le x_{\,4} \left( { \le 49} \right) \hfill \cr x_{\,1} + x_{\,2} + x_{\,3} + x_{\,4} = 49 \hfill \cr} \right.\quad \Rightarrow \cr & \Rightarrow \quad \left\{ \matrix{ x_{\,1} = y_{\,1} + 1\; \to \;0 \le y_{\,1} \le 7 \hfill \cr x_{\,2} = y_{\,2} + 3\; \to 0 \le y_{\,2} \le 6 \hfill \cr x_{\,3} = y_{\,3} + 10\; \to 0 \le y_{\,3} \le 10 \hfill \cr x_{\,4} = y_{\,4} \; \to 0 \le y_{\,4} \left( { \le 49} \right) \hfill \cr y_{\,1} + y_{\,2} + y_{\,3} + y_{\,4} = 49 - 14 = 35 \hfill \cr} \right.\quad \Rightarrow \cr & \Rightarrow \quad \left\{ \matrix{ 0 \le y_{\,1} \le 7 \hfill \cr 0 \le y_{\,2} \le 6 \hfill \cr 0 \le y_{\,3} \le 10 \hfill \cr y_{\,1} + y_{\,2} + y_{\,3} \le 35 \hfill \cr} \right. \cr} $$

Now, since the upper limits sum to $23 < 35$, then all the points inside the parallepiped $[0,7] \times [0,6] \times [0,10]$ respect the last inequality, thus $$ N = 8 \cdot 7 \cdot 11 = 616 $$

Answer 2

Well, just a quick search with Mathematica gives:

In[1]:=Length[Solve[{x1 + x2 + x3 + x4 == 49, 
   1 <= x1 <= 8 && 3 <= x2 <= 9 && 10 <= x3 <= 20 && 0 <= x4}, {x1, 
   x2, x3, x4}, Integers]]

Out[1]=616

So, there are $616$ solutions.

---

And the solutions are:

In[2]:=Solve[{x1 + x2 + x3 + x4 == 49, 
  1 <= x1 <= 8 && 3 <= x2 <= 9 && 10 <= x3 <= 20 && 0 <= x4}, {x1, x2,
   x3, x4}, Integers]

Out[2]={{x1 -> 1, x2 -> 3, x3 -> 10, x4 -> 35}, {x1 -> 1, x2 -> 3, x3 -> 11, 
  x4 -> 34}, {x1 -> 1, x2 -> 3, x3 -> 12, x4 -> 33}, {x1 -> 1, 
  x2 -> 3, x3 -> 13, x4 -> 32}, {x1 -> 1, x2 -> 3, x3 -> 14, 
  x4 -> 31}, {x1 -> 1, x2 -> 3, x3 -> 15, x4 -> 30}, {x1 -> 1, 
  x2 -> 3, x3 -> 16, x4 -> 29}, {x1 -> 1, x2 -> 3, x3 -> 17, 
  x4 -> 28}, {x1 -> 1, x2 -> 3, x3 -> 18, x4 -> 27}, {x1 -> 1, 
  x2 -> 3, x3 -> 19, x4 -> 26}, {x1 -> 1, x2 -> 3, x3 -> 20, 
  x4 -> 25}, {x1 -> 1, x2 -> 4, x3 -> 10, x4 -> 34}, {x1 -> 1, 
  x2 -> 4, x3 -> 11, x4 -> 33}, {x1 -> 1, x2 -> 4, x3 -> 12, 
  x4 -> 32}, {x1 -> 1, x2 -> 4, x3 -> 13, x4 -> 31}, {x1 -> 1, 
  x2 -> 4, x3 -> 14, x4 -> 30}, {x1 -> 1, x2 -> 4, x3 -> 15, 
  x4 -> 29}, {x1 -> 1, x2 -> 4, x3 -> 16, x4 -> 28}, {x1 -> 1, 
  x2 -> 4, x3 -> 17, x4 -> 27}, {x1 -> 1, x2 -> 4, x3 -> 18, 
  x4 -> 26}, {x1 -> 1, x2 -> 4, x3 -> 19, x4 -> 25}, {x1 -> 1, 
  x2 -> 4, x3 -> 20, x4 -> 24}, {x1 -> 1, x2 -> 5, x3 -> 10, 
  x4 -> 33}, {x1 -> 1, x2 -> 5, x3 -> 11, x4 -> 32}, {x1 -> 1, 
  x2 -> 5, x3 -> 12, x4 -> 31}, {x1 -> 1, x2 -> 5, x3 -> 13, 
  x4 -> 30}, {x1 -> 1, x2 -> 5, x3 -> 14, x4 -> 29}, {x1 -> 1, 
  x2 -> 5, x3 -> 15, x4 -> 28}, {x1 -> 1, x2 -> 5, x3 -> 16, 
  x4 -> 27}, {x1 -> 1, x2 -> 5, x3 -> 17, x4 -> 26}, {x1 -> 1, 
  x2 -> 5, x3 -> 18, x4 -> 25}, {x1 -> 1, x2 -> 5, x3 -> 19, 
  x4 -> 24}, {x1 -> 1, x2 -> 5, x3 -> 20, x4 -> 23}, {x1 -> 1, 
  x2 -> 6, x3 -> 10, x4 -> 32}, {x1 -> 1, x2 -> 6, x3 -> 11, 
  x4 -> 31}, {x1 -> 1, x2 -> 6, x3 -> 12, x4 -> 30}, {x1 -> 1, 
  x2 -> 6, x3 -> 13, x4 -> 29}, {x1 -> 1, x2 -> 6, x3 -> 14, 
  x4 -> 28}, {x1 -> 1, x2 -> 6, x3 -> 15, x4 -> 27}, {x1 -> 1, 
  x2 -> 6, x3 -> 16, x4 -> 26}, {x1 -> 1, x2 -> 6, x3 -> 17, 
  x4 -> 25}, {x1 -> 1, x2 -> 6, x3 -> 18, x4 -> 24}, {x1 -> 1, 
  x2 -> 6, x3 -> 19, x4 -> 23}, {x1 -> 1, x2 -> 6, x3 -> 20, 
  x4 -> 22}, {x1 -> 1, x2 -> 7, x3 -> 10, x4 -> 31}, {x1 -> 1, 
  x2 -> 7, x3 -> 11, x4 -> 30}, {x1 -> 1, x2 -> 7, x3 -> 12, 
  x4 -> 29}, {x1 -> 1, x2 -> 7, x3 -> 13, x4 -> 28}, {x1 -> 1, 
  x2 -> 7, x3 -> 14, x4 -> 27}, {x1 -> 1, x2 -> 7, x3 -> 15, 
  x4 -> 26}, {x1 -> 1, x2 -> 7, x3 -> 16, x4 -> 25}, {x1 -> 1, 
  x2 -> 7, x3 -> 17, x4 -> 24}, {x1 -> 1, x2 -> 7, x3 -> 18, 
  x4 -> 23}, {x1 -> 1, x2 -> 7, x3 -> 19, x4 -> 22}, {x1 -> 1, 
  x2 -> 7, x3 -> 20, x4 -> 21}, {x1 -> 1, x2 -> 8, x3 -> 10, 
  x4 -> 30}, {x1 -> 1, x2 -> 8, x3 -> 11, x4 -> 29}, {x1 -> 1, 
  x2 -> 8, x3 -> 12, x4 -> 28}, {x1 -> 1, x2 -> 8, x3 -> 13, 
  x4 -> 27}, {x1 -> 1, x2 -> 8, x3 -> 14, x4 -> 26}, {x1 -> 1, 
  x2 -> 8, x3 -> 15, x4 -> 25}, {x1 -> 1, x2 -> 8, x3 -> 16, 
  x4 -> 24}, {x1 -> 1, x2 -> 8, x3 -> 17, x4 -> 23}, {x1 -> 1, 
  x2 -> 8, x3 -> 18, x4 -> 22}, {x1 -> 1, x2 -> 8, x3 -> 19, 
  x4 -> 21}, {x1 -> 1, x2 -> 8, x3 -> 20, x4 -> 20}, {x1 -> 1, 
  x2 -> 9, x3 -> 10, x4 -> 29}, {x1 -> 1, x2 -> 9, x3 -> 11, 
  x4 -> 28}, {x1 -> 1, x2 -> 9, x3 -> 12, x4 -> 27}, {x1 -> 1, 
  x2 -> 9, x3 -> 13, x4 -> 26}, {x1 -> 1, x2 -> 9, x3 -> 14, 
  x4 -> 25}, {x1 -> 1, x2 -> 9, x3 -> 15, x4 -> 24}, {x1 -> 1, 
  x2 -> 9, x3 -> 16, x4 -> 23}, {x1 -> 1, x2 -> 9, x3 -> 17, 
  x4 -> 22}, {x1 -> 1, x2 -> 9, x3 -> 18, x4 -> 21}, {x1 -> 1, 
  x2 -> 9, x3 -> 19, x4 -> 20}, {x1 -> 1, x2 -> 9, x3 -> 20, 
  x4 -> 19}, {x1 -> 2, x2 -> 3, x3 -> 10, x4 -> 34}, {x1 -> 2, 
  x2 -> 3, x3 -> 11, x4 -> 33}, {x1 -> 2, x2 -> 3, x3 -> 12, 
  x4 -> 32}, {x1 -> 2, x2 -> 3, x3 -> 13, x4 -> 31}, {x1 -> 2, 
  x2 -> 3, x3 -> 14, x4 -> 30}, {x1 -> 2, x2 -> 3, x3 -> 15, 
  x4 -> 29}, {x1 -> 2, x2 -> 3, x3 -> 16, x4 -> 28}, {x1 -> 2, 
  x2 -> 3, x3 -> 17, x4 -> 27}, {x1 -> 2, x2 -> 3, x3 -> 18, 
  x4 -> 26}, {x1 -> 2, x2 -> 3, x3 -> 19, x4 -> 25}, {x1 -> 2, 
  x2 -> 3, x3 -> 20, x4 -> 24}, {x1 -> 2, x2 -> 4, x3 -> 10, 
  x4 -> 33}, {x1 -> 2, x2 -> 4, x3 -> 11, x4 -> 32}, {x1 -> 2, 
  x2 -> 4, x3 -> 12, x4 -> 31}, {x1 -> 2, x2 -> 4, x3 -> 13, 
  x4 -> 30}, {x1 -> 2, x2 -> 4, x3 -> 14, x4 -> 29}, {x1 -> 2, 
  x2 -> 4, x3 -> 15, x4 -> 28}, {x1 -> 2, x2 -> 4, x3 -> 16, 
  x4 -> 27}, {x1 -> 2, x2 -> 4, x3 -> 17, x4 -> 26}, {x1 -> 2, 
  x2 -> 4, x3 -> 18, x4 -> 25}, {x1 -> 2, x2 -> 4, x3 -> 19, 
  x4 -> 24}, {x1 -> 2, x2 -> 4, x3 -> 20, x4 -> 23}, {x1 -> 2, 
  x2 -> 5, x3 -> 10, x4 -> 32}, {x1 -> 2, x2 -> 5, x3 -> 11, 
  x4 -> 31}, {x1 -> 2, x2 -> 5, x3 -> 12, x4 -> 30}, {x1 -> 2, 
  x2 -> 5, x3 -> 13, x4 -> 29}, {x1 -> 2, x2 -> 5, x3 -> 14, 
  x4 -> 28}, {x1 -> 2, x2 -> 5, x3 -> 15, x4 -> 27}, {x1 -> 2, 
  x2 -> 5, x3 -> 16, x4 -> 26}, {x1 -> 2, x2 -> 5, x3 -> 17, 
  x4 -> 25}, {x1 -> 2, x2 -> 5, x3 -> 18, x4 -> 24}, {x1 -> 2, 
  x2 -> 5, x3 -> 19, x4 -> 23}, {x1 -> 2, x2 -> 5, x3 -> 20, 
  x4 -> 22}, {x1 -> 2, x2 -> 6, x3 -> 10, x4 -> 31}, {x1 -> 2, 
  x2 -> 6, x3 -> 11, x4 -> 30}, {x1 -> 2, x2 -> 6, x3 -> 12, 
  x4 -> 29}, {x1 -> 2, x2 -> 6, x3 -> 13, x4 -> 28}, {x1 -> 2, 
  x2 -> 6, x3 -> 14, x4 -> 27}, {x1 -> 2, x2 -> 6, x3 -> 15, 
  x4 -> 26}, {x1 -> 2, x2 -> 6, x3 -> 16, x4 -> 25}, {x1 -> 2, 
  x2 -> 6, x3 -> 17, x4 -> 24}, {x1 -> 2, x2 -> 6, x3 -> 18, 
  x4 -> 23}, {x1 -> 2, x2 -> 6, x3 -> 19, x4 -> 22}, {x1 -> 2, 
  x2 -> 6, x3 -> 20, x4 -> 21}, {x1 -> 2, x2 -> 7, x3 -> 10, 
  x4 -> 30}, {x1 -> 2, x2 -> 7, x3 -> 11, x4 -> 29}, {x1 -> 2, 
  x2 -> 7, x3 -> 12, x4 -> 28}, {x1 -> 2, x2 -> 7, x3 -> 13, 
  x4 -> 27}, {x1 -> 2, x2 -> 7, x3 -> 14, x4 -> 26}, {x1 -> 2, 
  x2 -> 7, x3 -> 15, x4 -> 25}, {x1 -> 2, x2 -> 7, x3 -> 16, 
  x4 -> 24}, {x1 -> 2, x2 -> 7, x3 -> 17, x4 -> 23}, {x1 -> 2, 
  x2 -> 7, x3 -> 18, x4 -> 22}, {x1 -> 2, x2 -> 7, x3 -> 19, 
  x4 -> 21}, {x1 -> 2, x2 -> 7, x3 -> 20, x4 -> 20}, {x1 -> 2, 
  x2 -> 8, x3 -> 10, x4 -> 29}, {x1 -> 2, x2 -> 8, x3 -> 11, 
  x4 -> 28}, {x1 -> 2, x2 -> 8, x3 -> 12, x4 -> 27}, {x1 -> 2, 
  x2 -> 8, x3 -> 13, x4 -> 26}, {x1 -> 2, x2 -> 8, x3 -> 14, 
  x4 -> 25}, {x1 -> 2, x2 -> 8, x3 -> 15, x4 -> 24}, {x1 -> 2, 
  x2 -> 8, x3 -> 16, x4 -> 23}, {x1 -> 2, x2 -> 8, x3 -> 17, 
  x4 -> 22}, {x1 -> 2, x2 -> 8, x3 -> 18, x4 -> 21}, {x1 -> 2, 
  x2 -> 8, x3 -> 19, x4 -> 20}, {x1 -> 2, x2 -> 8, x3 -> 20, 
  x4 -> 19}, {x1 -> 2, x2 -> 9, x3 -> 10, x4 -> 28}, {x1 -> 2, 
  x2 -> 9, x3 -> 11, x4 -> 27}, {x1 -> 2, x2 -> 9, x3 -> 12, 
  x4 -> 26}, {x1 -> 2, x2 -> 9, x3 -> 13, x4 -> 25}, {x1 -> 2, 
  x2 -> 9, x3 -> 14, x4 -> 24}, {x1 -> 2, x2 -> 9, x3 -> 15, 
  x4 -> 23}, {x1 -> 2, x2 -> 9, x3 -> 16, x4 -> 22}, {x1 -> 2, 
  x2 -> 9, x3 -> 17, x4 -> 21}, {x1 -> 2, x2 -> 9, x3 -> 18, 
  x4 -> 20}, {x1 -> 2, x2 -> 9, x3 -> 19, x4 -> 19}, {x1 -> 2, 
  x2 -> 9, x3 -> 20, x4 -> 18}, {x1 -> 3, x2 -> 3, x3 -> 10, 
  x4 -> 33}, {x1 -> 3, x2 -> 3, x3 -> 11, x4 -> 32}, {x1 -> 3, 
  x2 -> 3, x3 -> 12, x4 -> 31}, {x1 -> 3, x2 -> 3, x3 -> 13, 
  x4 -> 30}, {x1 -> 3, x2 -> 3, x3 -> 14, x4 -> 29}, {x1 -> 3, 
  x2 -> 3, x3 -> 15, x4 -> 28}, {x1 -> 3, x2 -> 3, x3 -> 16, 
  x4 -> 27}, {x1 -> 3, x2 -> 3, x3 -> 17, x4 -> 26}, {x1 -> 3, 
  x2 -> 3, x3 -> 18, x4 -> 25}, {x1 -> 3, x2 -> 3, x3 -> 19, 
  x4 -> 24}, {x1 -> 3, x2 -> 3, x3 -> 20, x4 -> 23}, {x1 -> 3, 
  x2 -> 4, x3 -> 10, x4 -> 32}, {x1 -> 3, x2 -> 4, x3 -> 11, 
  x4 -> 31}, {x1 -> 3, x2 -> 4, x3 -> 12, x4 -> 30}, {x1 -> 3, 
  x2 -> 4, x3 -> 13, x4 -> 29}, {x1 -> 3, x2 -> 4, x3 -> 14, 
  x4 -> 28}, {x1 -> 3, x2 -> 4, x3 -> 15, x4 -> 27}, {x1 -> 3, 
  x2 -> 4, x3 -> 16, x4 -> 26}, {x1 -> 3, x2 -> 4, x3 -> 17, 
  x4 -> 25}, {x1 -> 3, x2 -> 4, x3 -> 18, x4 -> 24}, {x1 -> 3, 
  x2 -> 4, x3 -> 19, x4 -> 23}, {x1 -> 3, x2 -> 4, x3 -> 20, 
  x4 -> 22}, {x1 -> 3, x2 -> 5, x3 -> 10, x4 -> 31}, {x1 -> 3, 
  x2 -> 5, x3 -> 11, x4 -> 30}, {x1 -> 3, x2 -> 5, x3 -> 12, 
  x4 -> 29}, {x1 -> 3, x2 -> 5, x3 -> 13, x4 -> 28}, {x1 -> 3, 
  x2 -> 5, x3 -> 14, x4 -> 27}, {x1 -> 3, x2 -> 5, x3 -> 15, 
  x4 -> 26}, {x1 -> 3, x2 -> 5, x3 -> 16, x4 -> 25}, {x1 -> 3, 
  x2 -> 5, x3 -> 17, x4 -> 24}, {x1 -> 3, x2 -> 5, x3 -> 18, 
  x4 -> 23}, {x1 -> 3, x2 -> 5, x3 -> 19, x4 -> 22}, {x1 -> 3, 
  x2 -> 5, x3 -> 20, x4 -> 21}, {x1 -> 3, x2 -> 6, x3 -> 10, 
  x4 -> 30}, {x1 -> 3, x2 -> 6, x3 -> 11, x4 -> 29}, {x1 -> 3, 
  x2 -> 6, x3 -> 12, x4 -> 28}, {x1 -> 3, x2 -> 6, x3 -> 13, 
  x4 -> 27}, {x1 -> 3, x2 -> 6, x3 -> 14, x4 -> 26}, {x1 -> 3, 
  x2 -> 6, x3 -> 15, x4 -> 25}, {x1 -> 3, x2 -> 6, x3 -> 16, 
  x4 -> 24}, {x1 -> 3, x2 -> 6, x3 -> 17, x4 -> 23}, {x1 -> 3, 
  x2 -> 6, x3 -> 18, x4 -> 22}, {x1 -> 3, x2 -> 6, x3 -> 19, 
  x4 -> 21}, {x1 -> 3, x2 -> 6, x3 -> 20, x4 -> 20}, {x1 -> 3, 
  x2 -> 7, x3 -> 10, x4 -> 29}, {x1 -> 3, x2 -> 7, x3 -> 11, 
  x4 -> 28}, {x1 -> 3, x2 -> 7, x3 -> 12, x4 -> 27}, {x1 -> 3, 
  x2 -> 7, x3 -> 13, x4 -> 26}, {x1 -> 3, x2 -> 7, x3 -> 14, 
  x4 -> 25}, {x1 -> 3, x2 -> 7, x3 -> 15, x4 -> 24}, {x1 -> 3, 
  x2 -> 7, x3 -> 16, x4 -> 23}, {x1 -> 3, x2 -> 7, x3 -> 17, 
  x4 -> 22}, {x1 -> 3, x2 -> 7, x3 -> 18, x4 -> 21}, {x1 -> 3, 
  x2 -> 7, x3 -> 19, x4 -> 20}, {x1 -> 3, x2 -> 7, x3 -> 20, 
  x4 -> 19}, {x1 -> 3, x2 -> 8, x3 -> 10, x4 -> 28}, {x1 -> 3, 
  x2 -> 8, x3 -> 11, x4 -> 27}, {x1 -> 3, x2 -> 8, x3 -> 12, 
  x4 -> 26}, {x1 -> 3, x2 -> 8, x3 -> 13, x4 -> 25}, {x1 -> 3, 
  x2 -> 8, x3 -> 14, x4 -> 24}, {x1 -> 3, x2 -> 8, x3 -> 15, 
  x4 -> 23}, {x1 -> 3, x2 -> 8, x3 -> 16, x4 -> 22}, {x1 -> 3, 
  x2 -> 8, x3 -> 17, x4 -> 21}, {x1 -> 3, x2 -> 8, x3 -> 18, 
  x4 -> 20}, {x1 -> 3, x2 -> 8, x3 -> 19, x4 -> 19}, {x1 -> 3, 
  x2 -> 8, x3 -> 20, x4 -> 18}, {x1 -> 3, x2 -> 9, x3 -> 10, 
  x4 -> 27}, {x1 -> 3, x2 -> 9, x3 -> 11, x4 -> 26}, {x1 -> 3, 
  x2 -> 9, x3 -> 12, x4 -> 25}, {x1 -> 3, x2 -> 9, x3 -> 13, 
  x4 -> 24}, {x1 -> 3, x2 -> 9, x3 -> 14, x4 -> 23}, {x1 -> 3, 
  x2 -> 9, x3 -> 15, x4 -> 22}, {x1 -> 3, x2 -> 9, x3 -> 16, 
  x4 -> 21}, {x1 -> 3, x2 -> 9, x3 -> 17, x4 -> 20}, {x1 -> 3, 
  x2 -> 9, x3 -> 18, x4 -> 19}, {x1 -> 3, x2 -> 9, x3 -> 19, 
  x4 -> 18}, {x1 -> 3, x2 -> 9, x3 -> 20, x4 -> 17}, {x1 -> 4, 
  x2 -> 3, x3 -> 10, x4 -> 32}, {x1 -> 4, x2 -> 3, x3 -> 11, 
  x4 -> 31}, {x1 -> 4, x2 -> 3, x3 -> 12, x4 -> 30}, {x1 -> 4, 
  x2 -> 3, x3 -> 13, x4 -> 29}, {x1 -> 4, x2 -> 3, x3 -> 14, 
  x4 -> 28}, {x1 -> 4, x2 -> 3, x3 -> 15, x4 -> 27}, {x1 -> 4, 
  x2 -> 3, x3 -> 16, x4 -> 26}, {x1 -> 4, x2 -> 3, x3 -> 17, 
  x4 -> 25}, {x1 -> 4, x2 -> 3, x3 -> 18, x4 -> 24}, {x1 -> 4, 
  x2 -> 3, x3 -> 19, x4 -> 23}, {x1 -> 4, x2 -> 3, x3 -> 20, 
  x4 -> 22}, {x1 -> 4, x2 -> 4, x3 -> 10, x4 -> 31}, {x1 -> 4, 
  x2 -> 4, x3 -> 11, x4 -> 30}, {x1 -> 4, x2 -> 4, x3 -> 12, 
  x4 -> 29}, {x1 -> 4, x2 -> 4, x3 -> 13, x4 -> 28}, {x1 -> 4, 
  x2 -> 4, x3 -> 14, x4 -> 27}, {x1 -> 4, x2 -> 4, x3 -> 15, 
  x4 -> 26}, {x1 -> 4, x2 -> 4, x3 -> 16, x4 -> 25}, {x1 -> 4, 
  x2 -> 4, x3 -> 17, x4 -> 24}, {x1 -> 4, x2 -> 4, x3 -> 18, 
  x4 -> 23}, {x1 -> 4, x2 -> 4, x3 -> 19, x4 -> 22}, {x1 -> 4, 
  x2 -> 4, x3 -> 20, x4 -> 21}, {x1 -> 4, x2 -> 5, x3 -> 10, 
  x4 -> 30}, {x1 -> 4, x2 -> 5, x3 -> 11, x4 -> 29}, {x1 -> 4, 
  x2 -> 5, x3 -> 12, x4 -> 28}, {x1 -> 4, x2 -> 5, x3 -> 13, 
  x4 -> 27}, {x1 -> 4, x2 -> 5, x3 -> 14, x4 -> 26}, {x1 -> 4, 
  x2 -> 5, x3 -> 15, x4 -> 25}, {x1 -> 4, x2 -> 5, x3 -> 16, 
  x4 -> 24}, {x1 -> 4, x2 -> 5, x3 -> 17, x4 -> 23}, {x1 -> 4, 
  x2 -> 5, x3 -> 18, x4 -> 22}, {x1 -> 4, x2 -> 5, x3 -> 19, 
  x4 -> 21}, {x1 -> 4, x2 -> 5, x3 -> 20, x4 -> 20}, {x1 -> 4, 
  x2 -> 6, x3 -> 10, x4 -> 29}, {x1 -> 4, x2 -> 6, x3 -> 11, 
  x4 -> 28}, {x1 -> 4, x2 -> 6, x3 -> 12, x4 -> 27}, {x1 -> 4, 
  x2 -> 6, x3 -> 13, x4 -> 26}, {x1 -> 4, x2 -> 6, x3 -> 14, 
  x4 -> 25}, {x1 -> 4, x2 -> 6, x3 -> 15, x4 -> 24}, {x1 -> 4, 
  x2 -> 6, x3 -> 16, x4 -> 23}, {x1 -> 4, x2 -> 6, x3 -> 17, 
  x4 -> 22}, {x1 -> 4, x2 -> 6, x3 -> 18, x4 -> 21}, {x1 -> 4, 
  x2 -> 6, x3 -> 19, x4 -> 20}, {x1 -> 4, x2 -> 6, x3 -> 20, 
  x4 -> 19}, {x1 -> 4, x2 -> 7, x3 -> 10, x4 -> 28}, {x1 -> 4, 
  x2 -> 7, x3 -> 11, x4 -> 27}, {x1 -> 4, x2 -> 7, x3 -> 12, 
  x4 -> 26}, {x1 -> 4, x2 -> 7, x3 -> 13, x4 -> 25}, {x1 -> 4, 
  x2 -> 7, x3 -> 14, x4 -> 24}, {x1 -> 4, x2 -> 7, x3 -> 15, 
  x4 -> 23}, {x1 -> 4, x2 -> 7, x3 -> 16, x4 -> 22}, {x1 -> 4, 
  x2 -> 7, x3 -> 17, x4 -> 21}, {x1 -> 4, x2 -> 7, x3 -> 18, 
  x4 -> 20}, {x1 -> 4, x2 -> 7, x3 -> 19, x4 -> 19}, {x1 -> 4, 
  x2 -> 7, x3 -> 20, x4 -> 18}, {x1 -> 4, x2 -> 8, x3 -> 10, 
  x4 -> 27}, {x1 -> 4, x2 -> 8, x3 -> 11, x4 -> 26}, {x1 -> 4, 
  x2 -> 8, x3 -> 12, x4 -> 25}, {x1 -> 4, x2 -> 8, x3 -> 13, 
  x4 -> 24}, {x1 -> 4, x2 -> 8, x3 -> 14, x4 -> 23}, {x1 -> 4, 
  x2 -> 8, x3 -> 15, x4 -> 22}, {x1 -> 4, x2 -> 8, x3 -> 16, 
  x4 -> 21}, {x1 -> 4, x2 -> 8, x3 -> 17, x4 -> 20}, {x1 -> 4, 
  x2 -> 8, x3 -> 18, x4 -> 19}, {x1 -> 4, x2 -> 8, x3 -> 19, 
  x4 -> 18}, {x1 -> 4, x2 -> 8, x3 -> 20, x4 -> 17}, {x1 -> 4, 
  x2 -> 9, x3 -> 10, x4 -> 26}, {x1 -> 4, x2 -> 9, x3 -> 11, 
  x4 -> 25}, {x1 -> 4, x2 -> 9, x3 -> 12, x4 -> 24}, {x1 -> 4, 
  x2 -> 9, x3 -> 13, x4 -> 23}, {x1 -> 4, x2 -> 9, x3 -> 14, 
  x4 -> 22}, {x1 -> 4, x2 -> 9, x3 -> 15, x4 -> 21}, {x1 -> 4, 
  x2 -> 9, x3 -> 16, x4 -> 20}, {x1 -> 4, x2 -> 9, x3 -> 17, 
  x4 -> 19}, {x1 -> 4, x2 -> 9, x3 -> 18, x4 -> 18}, {x1 -> 4, 
  x2 -> 9, x3 -> 19, x4 -> 17}, {x1 -> 4, x2 -> 9, x3 -> 20, 
  x4 -> 16}, {x1 -> 5, x2 -> 3, x3 -> 10, x4 -> 31}, {x1 -> 5, 
  x2 -> 3, x3 -> 11, x4 -> 30}, {x1 -> 5, x2 -> 3, x3 -> 12, 
  x4 -> 29}, {x1 -> 5, x2 -> 3, x3 -> 13, x4 -> 28}, {x1 -> 5, 
  x2 -> 3, x3 -> 14, x4 -> 27}, {x1 -> 5, x2 -> 3, x3 -> 15, 
  x4 -> 26}, {x1 -> 5, x2 -> 3, x3 -> 16, x4 -> 25}, {x1 -> 5, 
  x2 -> 3, x3 -> 17, x4 -> 24}, {x1 -> 5, x2 -> 3, x3 -> 18, 
  x4 -> 23}, {x1 -> 5, x2 -> 3, x3 -> 19, x4 -> 22}, {x1 -> 5, 
  x2 -> 3, x3 -> 20, x4 -> 21}, {x1 -> 5, x2 -> 4, x3 -> 10, 
  x4 -> 30}, {x1 -> 5, x2 -> 4, x3 -> 11, x4 -> 29}, {x1 -> 5, 
  x2 -> 4, x3 -> 12, x4 -> 28}, {x1 -> 5, x2 -> 4, x3 -> 13, 
  x4 -> 27}, {x1 -> 5, x2 -> 4, x3 -> 14, x4 -> 26}, {x1 -> 5, 
  x2 -> 4, x3 -> 15, x4 -> 25}, {x1 -> 5, x2 -> 4, x3 -> 16, 
  x4 -> 24}, {x1 -> 5, x2 -> 4, x3 -> 17, x4 -> 23}, {x1 -> 5, 
  x2 -> 4, x3 -> 18, x4 -> 22}, {x1 -> 5, x2 -> 4, x3 -> 19, 
  x4 -> 21}, {x1 -> 5, x2 -> 4, x3 -> 20, x4 -> 20}, {x1 -> 5, 
  x2 -> 5, x3 -> 10, x4 -> 29}, {x1 -> 5, x2 -> 5, x3 -> 11, 
  x4 -> 28}, {x1 -> 5, x2 -> 5, x3 -> 12, x4 -> 27}, {x1 -> 5, 
  x2 -> 5, x3 -> 13, x4 -> 26}, {x1 -> 5, x2 -> 5, x3 -> 14, 
  x4 -> 25}, {x1 -> 5, x2 -> 5, x3 -> 15, x4 -> 24}, {x1 -> 5, 
  x2 -> 5, x3 -> 16, x4 -> 23}, {x1 -> 5, x2 -> 5, x3 -> 17, 
  x4 -> 22}, {x1 -> 5, x2 -> 5, x3 -> 18, x4 -> 21}, {x1 -> 5, 
  x2 -> 5, x3 -> 19, x4 -> 20}, {x1 -> 5, x2 -> 5, x3 -> 20, 
  x4 -> 19}, {x1 -> 5, x2 -> 6, x3 -> 10, x4 -> 28}, {x1 -> 5, 
  x2 -> 6, x3 -> 11, x4 -> 27}, {x1 -> 5, x2 -> 6, x3 -> 12, 
  x4 -> 26}, {x1 -> 5, x2 -> 6, x3 -> 13, x4 -> 25}, {x1 -> 5, 
  x2 -> 6, x3 -> 14, x4 -> 24}, {x1 -> 5, x2 -> 6, x3 -> 15, 
  x4 -> 23}, {x1 -> 5, x2 -> 6, x3 -> 16, x4 -> 22}, {x1 -> 5, 
  x2 -> 6, x3 -> 17, x4 -> 21}, {x1 -> 5, x2 -> 6, x3 -> 18, 
  x4 -> 20}, {x1 -> 5, x2 -> 6, x3 -> 19, x4 -> 19}, {x1 -> 5, 
  x2 -> 6, x3 -> 20, x4 -> 18}, {x1 -> 5, x2 -> 7, x3 -> 10, 
  x4 -> 27}, {x1 -> 5, x2 -> 7, x3 -> 11, x4 -> 26}, {x1 -> 5, 
  x2 -> 7, x3 -> 12, x4 -> 25}, {x1 -> 5, x2 -> 7, x3 -> 13, 
  x4 -> 24}, {x1 -> 5, x2 -> 7, x3 -> 14, x4 -> 23}, {x1 -> 5, 
  x2 -> 7, x3 -> 15, x4 -> 22}, {x1 -> 5, x2 -> 7, x3 -> 16, 
  x4 -> 21}, {x1 -> 5, x2 -> 7, x3 -> 17, x4 -> 20}, {x1 -> 5, 
  x2 -> 7, x3 -> 18, x4 -> 19}, {x1 -> 5, x2 -> 7, x3 -> 19, 
  x4 -> 18}, {x1 -> 5, x2 -> 7, x3 -> 20, x4 -> 17}, {x1 -> 5, 
  x2 -> 8, x3 -> 10, x4 -> 26}, {x1 -> 5, x2 -> 8, x3 -> 11, 
  x4 -> 25}, {x1 -> 5, x2 -> 8, x3 -> 12, x4 -> 24}, {x1 -> 5, 
  x2 -> 8, x3 -> 13, x4 -> 23}, {x1 -> 5, x2 -> 8, x3 -> 14, 
  x4 -> 22}, {x1 -> 5, x2 -> 8, x3 -> 15, x4 -> 21}, {x1 -> 5, 
  x2 -> 8, x3 -> 16, x4 -> 20}, {x1 -> 5, x2 -> 8, x3 -> 17, 
  x4 -> 19}, {x1 -> 5, x2 -> 8, x3 -> 18, x4 -> 18}, {x1 -> 5, 
  x2 -> 8, x3 -> 19, x4 -> 17}, {x1 -> 5, x2 -> 8, x3 -> 20, 
  x4 -> 16}, {x1 -> 5, x2 -> 9, x3 -> 10, x4 -> 25}, {x1 -> 5, 
  x2 -> 9, x3 -> 11, x4 -> 24}, {x1 -> 5, x2 -> 9, x3 -> 12, 
  x4 -> 23}, {x1 -> 5, x2 -> 9, x3 -> 13, x4 -> 22}, {x1 -> 5, 
  x2 -> 9, x3 -> 14, x4 -> 21}, {x1 -> 5, x2 -> 9, x3 -> 15, 
  x4 -> 20}, {x1 -> 5, x2 -> 9, x3 -> 16, x4 -> 19}, {x1 -> 5, 
  x2 -> 9, x3 -> 17, x4 -> 18}, {x1 -> 5, x2 -> 9, x3 -> 18, 
  x4 -> 17}, {x1 -> 5, x2 -> 9, x3 -> 19, x4 -> 16}, {x1 -> 5, 
  x2 -> 9, x3 -> 20, x4 -> 15}, {x1 -> 6, x2 -> 3, x3 -> 10, 
  x4 -> 30}, {x1 -> 6, x2 -> 3, x3 -> 11, x4 -> 29}, {x1 -> 6, 
  x2 -> 3, x3 -> 12, x4 -> 28}, {x1 -> 6, x2 -> 3, x3 -> 13, 
  x4 -> 27}, {x1 -> 6, x2 -> 3, x3 -> 14, x4 -> 26}, {x1 -> 6, 
  x2 -> 3, x3 -> 15, x4 -> 25}, {x1 -> 6, x2 -> 3, x3 -> 16, 
  x4 -> 24}, {x1 -> 6, x2 -> 3, x3 -> 17, x4 -> 23}, {x1 -> 6, 
  x2 -> 3, x3 -> 18, x4 -> 22}, {x1 -> 6, x2 -> 3, x3 -> 19, 
  x4 -> 21}, {x1 -> 6, x2 -> 3, x3 -> 20, x4 -> 20}, {x1 -> 6, 
  x2 -> 4, x3 -> 10, x4 -> 29}, {x1 -> 6, x2 -> 4, x3 -> 11, 
  x4 -> 28}, {x1 -> 6, x2 -> 4, x3 -> 12, x4 -> 27}, {x1 -> 6, 
  x2 -> 4, x3 -> 13, x4 -> 26}, {x1 -> 6, x2 -> 4, x3 -> 14, 
  x4 -> 25}, {x1 -> 6, x2 -> 4, x3 -> 15, x4 -> 24}, {x1 -> 6, 
  x2 -> 4, x3 -> 16, x4 -> 23}, {x1 -> 6, x2 -> 4, x3 -> 17, 
  x4 -> 22}, {x1 -> 6, x2 -> 4, x3 -> 18, x4 -> 21}, {x1 -> 6, 
  x2 -> 4, x3 -> 19, x4 -> 20}, {x1 -> 6, x2 -> 4, x3 -> 20, 
  x4 -> 19}, {x1 -> 6, x2 -> 5, x3 -> 10, x4 -> 28}, {x1 -> 6, 
  x2 -> 5, x3 -> 11, x4 -> 27}, {x1 -> 6, x2 -> 5, x3 -> 12, 
  x4 -> 26}, {x1 -> 6, x2 -> 5, x3 -> 13, x4 -> 25}, {x1 -> 6, 
  x2 -> 5, x3 -> 14, x4 -> 24}, {x1 -> 6, x2 -> 5, x3 -> 15, 
  x4 -> 23}, {x1 -> 6, x2 -> 5, x3 -> 16, x4 -> 22}, {x1 -> 6, 
  x2 -> 5, x3 -> 17, x4 -> 21}, {x1 -> 6, x2 -> 5, x3 -> 18, 
  x4 -> 20}, {x1 -> 6, x2 -> 5, x3 -> 19, x4 -> 19}, {x1 -> 6, 
  x2 -> 5, x3 -> 20, x4 -> 18}, {x1 -> 6, x2 -> 6, x3 -> 10, 
  x4 -> 27}, {x1 -> 6, x2 -> 6, x3 -> 11, x4 -> 26}, {x1 -> 6, 
  x2 -> 6, x3 -> 12, x4 -> 25}, {x1 -> 6, x2 -> 6, x3 -> 13, 
  x4 -> 24}, {x1 -> 6, x2 -> 6, x3 -> 14, x4 -> 23}, {x1 -> 6, 
  x2 -> 6, x3 -> 15, x4 -> 22}, {x1 -> 6, x2 -> 6, x3 -> 16, 
  x4 -> 21}, {x1 -> 6, x2 -> 6, x3 -> 17, x4 -> 20}, {x1 -> 6, 
  x2 -> 6, x3 -> 18, x4 -> 19}, {x1 -> 6, x2 -> 6, x3 -> 19, 
  x4 -> 18}, {x1 -> 6, x2 -> 6, x3 -> 20, x4 -> 17}, {x1 -> 6, 
  x2 -> 7, x3 -> 10, x4 -> 26}, {x1 -> 6, x2 -> 7, x3 -> 11, 
  x4 -> 25}, {x1 -> 6, x2 -> 7, x3 -> 12, x4 -> 24}, {x1 -> 6, 
  x2 -> 7, x3 -> 13, x4 -> 23}, {x1 -> 6, x2 -> 7, x3 -> 14, 
  x4 -> 22}, {x1 -> 6, x2 -> 7, x3 -> 15, x4 -> 21}, {x1 -> 6, 
  x2 -> 7, x3 -> 16, x4 -> 20}, {x1 -> 6, x2 -> 7, x3 -> 17, 
  x4 -> 19}, {x1 -> 6, x2 -> 7, x3 -> 18, x4 -> 18}, {x1 -> 6, 
  x2 -> 7, x3 -> 19, x4 -> 17}, {x1 -> 6, x2 -> 7, x3 -> 20, 
  x4 -> 16}, {x1 -> 6, x2 -> 8, x3 -> 10, x4 -> 25}, {x1 -> 6, 
  x2 -> 8, x3 -> 11, x4 -> 24}, {x1 -> 6, x2 -> 8, x3 -> 12, 
  x4 -> 23}, {x1 -> 6, x2 -> 8, x3 -> 13, x4 -> 22}, {x1 -> 6, 
  x2 -> 8, x3 -> 14, x4 -> 21}, {x1 -> 6, x2 -> 8, x3 -> 15, 
  x4 -> 20}, {x1 -> 6, x2 -> 8, x3 -> 16, x4 -> 19}, {x1 -> 6, 
  x2 -> 8, x3 -> 17, x4 -> 18}, {x1 -> 6, x2 -> 8, x3 -> 18, 
  x4 -> 17}, {x1 -> 6, x2 -> 8, x3 -> 19, x4 -> 16}, {x1 -> 6, 
  x2 -> 8, x3 -> 20, x4 -> 15}, {x1 -> 6, x2 -> 9, x3 -> 10, 
  x4 -> 24}, {x1 -> 6, x2 -> 9, x3 -> 11, x4 -> 23}, {x1 -> 6, 
  x2 -> 9, x3 -> 12, x4 -> 22}, {x1 -> 6, x2 -> 9, x3 -> 13, 
  x4 -> 21}, {x1 -> 6, x2 -> 9, x3 -> 14, x4 -> 20}, {x1 -> 6, 
  x2 -> 9, x3 -> 15, x4 -> 19}, {x1 -> 6, x2 -> 9, x3 -> 16, 
  x4 -> 18}, {x1 -> 6, x2 -> 9, x3 -> 17, x4 -> 17}, {x1 -> 6, 
  x2 -> 9, x3 -> 18, x4 -> 16}, {x1 -> 6, x2 -> 9, x3 -> 19, 
  x4 -> 15}, {x1 -> 6, x2 -> 9, x3 -> 20, x4 -> 14}, {x1 -> 7, 
  x2 -> 3, x3 -> 10, x4 -> 29}, {x1 -> 7, x2 -> 3, x3 -> 11, 
  x4 -> 28}, {x1 -> 7, x2 -> 3, x3 -> 12, x4 -> 27}, {x1 -> 7, 
  x2 -> 3, x3 -> 13, x4 -> 26}, {x1 -> 7, x2 -> 3, x3 -> 14, 
  x4 -> 25}, {x1 -> 7, x2 -> 3, x3 -> 15, x4 -> 24}, {x1 -> 7, 
  x2 -> 3, x3 -> 16, x4 -> 23}, {x1 -> 7, x2 -> 3, x3 -> 17, 
  x4 -> 22}, {x1 -> 7, x2 -> 3, x3 -> 18, x4 -> 21}, {x1 -> 7, 
  x2 -> 3, x3 -> 19, x4 -> 20}, {x1 -> 7, x2 -> 3, x3 -> 20, 
  x4 -> 19}, {x1 -> 7, x2 -> 4, x3 -> 10, x4 -> 28}, {x1 -> 7, 
  x2 -> 4, x3 -> 11, x4 -> 27}, {x1 -> 7, x2 -> 4, x3 -> 12, 
  x4 -> 26}, {x1 -> 7, x2 -> 4, x3 -> 13, x4 -> 25}, {x1 -> 7, 
  x2 -> 4, x3 -> 14, x4 -> 24}, {x1 -> 7, x2 -> 4, x3 -> 15, 
  x4 -> 23}, {x1 -> 7, x2 -> 4, x3 -> 16, x4 -> 22}, {x1 -> 7, 
  x2 -> 4, x3 -> 17, x4 -> 21}, {x1 -> 7, x2 -> 4, x3 -> 18, 
  x4 -> 20}, {x1 -> 7, x2 -> 4, x3 -> 19, x4 -> 19}, {x1 -> 7, 
  x2 -> 4, x3 -> 20, x4 -> 18}, {x1 -> 7, x2 -> 5, x3 -> 10, 
  x4 -> 27}, {x1 -> 7, x2 -> 5, x3 -> 11, x4 -> 26}, {x1 -> 7, 
  x2 -> 5, x3 -> 12, x4 -> 25}, {x1 -> 7, x2 -> 5, x3 -> 13, 
  x4 -> 24}, {x1 -> 7, x2 -> 5, x3 -> 14, x4 -> 23}, {x1 -> 7, 
  x2 -> 5, x3 -> 15, x4 -> 22}, {x1 -> 7, x2 -> 5, x3 -> 16, 
  x4 -> 21}, {x1 -> 7, x2 -> 5, x3 -> 17, x4 -> 20}, {x1 -> 7, 
  x2 -> 5, x3 -> 18, x4 -> 19}, {x1 -> 7, x2 -> 5, x3 -> 19, 
  x4 -> 18}, {x1 -> 7, x2 -> 5, x3 -> 20, x4 -> 17}, {x1 -> 7, 
  x2 -> 6, x3 -> 10, x4 -> 26}, {x1 -> 7, x2 -> 6, x3 -> 11, 
  x4 -> 25}, {x1 -> 7, x2 -> 6, x3 -> 12, x4 -> 24}, {x1 -> 7, 
  x2 -> 6, x3 -> 13, x4 -> 23}, {x1 -> 7, x2 -> 6, x3 -> 14, 
  x4 -> 22}, {x1 -> 7, x2 -> 6, x3 -> 15, x4 -> 21}, {x1 -> 7, 
  x2 -> 6, x3 -> 16, x4 -> 20}, {x1 -> 7, x2 -> 6, x3 -> 17, 
  x4 -> 19}, {x1 -> 7, x2 -> 6, x3 -> 18, x4 -> 18}, {x1 -> 7, 
  x2 -> 6, x3 -> 19, x4 -> 17}, {x1 -> 7, x2 -> 6, x3 -> 20, 
  x4 -> 16}, {x1 -> 7, x2 -> 7, x3 -> 10, x4 -> 25}, {x1 -> 7, 
  x2 -> 7, x3 -> 11, x4 -> 24}, {x1 -> 7, x2 -> 7, x3 -> 12, 
  x4 -> 23}, {x1 -> 7, x2 -> 7, x3 -> 13, x4 -> 22}, {x1 -> 7, 
  x2 -> 7, x3 -> 14, x4 -> 21}, {x1 -> 7, x2 -> 7, x3 -> 15, 
  x4 -> 20}, {x1 -> 7, x2 -> 7, x3 -> 16, x4 -> 19}, {x1 -> 7, 
  x2 -> 7, x3 -> 17, x4 -> 18}, {x1 -> 7, x2 -> 7, x3 -> 18, 
  x4 -> 17}, {x1 -> 7, x2 -> 7, x3 -> 19, x4 -> 16}, {x1 -> 7, 
  x2 -> 7, x3 -> 20, x4 -> 15}, {x1 -> 7, x2 -> 8, x3 -> 10, 
  x4 -> 24}, {x1 -> 7, x2 -> 8, x3 -> 11, x4 -> 23}, {x1 -> 7, 
  x2 -> 8, x3 -> 12, x4 -> 22}, {x1 -> 7, x2 -> 8, x3 -> 13, 
  x4 -> 21}, {x1 -> 7, x2 -> 8, x3 -> 14, x4 -> 20}, {x1 -> 7, 
  x2 -> 8, x3 -> 15, x4 -> 19}, {x1 -> 7, x2 -> 8, x3 -> 16, 
  x4 -> 18}, {x1 -> 7, x2 -> 8, x3 -> 17, x4 -> 17}, {x1 -> 7, 
  x2 -> 8, x3 -> 18, x4 -> 16}, {x1 -> 7, x2 -> 8, x3 -> 19, 
  x4 -> 15}, {x1 -> 7, x2 -> 8, x3 -> 20, x4 -> 14}, {x1 -> 7, 
  x2 -> 9, x3 -> 10, x4 -> 23}, {x1 -> 7, x2 -> 9, x3 -> 11, 
  x4 -> 22}, {x1 -> 7, x2 -> 9, x3 -> 12, x4 -> 21}, {x1 -> 7, 
  x2 -> 9, x3 -> 13, x4 -> 20}, {x1 -> 7, x2 -> 9, x3 -> 14, 
  x4 -> 19}, {x1 -> 7, x2 -> 9, x3 -> 15, x4 -> 18}, {x1 -> 7, 
  x2 -> 9, x3 -> 16, x4 -> 17}, {x1 -> 7, x2 -> 9, x3 -> 17, 
  x4 -> 16}, {x1 -> 7, x2 -> 9, x3 -> 18, x4 -> 15}, {x1 -> 7, 
  x2 -> 9, x3 -> 19, x4 -> 14}, {x1 -> 7, x2 -> 9, x3 -> 20, 
  x4 -> 13}, {x1 -> 8, x2 -> 3, x3 -> 10, x4 -> 28}, {x1 -> 8, 
  x2 -> 3, x3 -> 11, x4 -> 27}, {x1 -> 8, x2 -> 3, x3 -> 12, 
  x4 -> 26}, {x1 -> 8, x2 -> 3, x3 -> 13, x4 -> 25}, {x1 -> 8, 
  x2 -> 3, x3 -> 14, x4 -> 24}, {x1 -> 8, x2 -> 3, x3 -> 15, 
  x4 -> 23}, {x1 -> 8, x2 -> 3, x3 -> 16, x4 -> 22}, {x1 -> 8, 
  x2 -> 3, x3 -> 17, x4 -> 21}, {x1 -> 8, x2 -> 3, x3 -> 18, 
  x4 -> 20}, {x1 -> 8, x2 -> 3, x3 -> 19, x4 -> 19}, {x1 -> 8, 
  x2 -> 3, x3 -> 20, x4 -> 18}, {x1 -> 8, x2 -> 4, x3 -> 10, 
  x4 -> 27}, {x1 -> 8, x2 -> 4, x3 -> 11, x4 -> 26}, {x1 -> 8, 
  x2 -> 4, x3 -> 12, x4 -> 25}, {x1 -> 8, x2 -> 4, x3 -> 13, 
  x4 -> 24}, {x1 -> 8, x2 -> 4, x3 -> 14, x4 -> 23}, {x1 -> 8, 
  x2 -> 4, x3 -> 15, x4 -> 22}, {x1 -> 8, x2 -> 4, x3 -> 16, 
  x4 -> 21}, {x1 -> 8, x2 -> 4, x3 -> 17, x4 -> 20}, {x1 -> 8, 
  x2 -> 4, x3 -> 18, x4 -> 19}, {x1 -> 8, x2 -> 4, x3 -> 19, 
  x4 -> 18}, {x1 -> 8, x2 -> 4, x3 -> 20, x4 -> 17}, {x1 -> 8, 
  x2 -> 5, x3 -> 10, x4 -> 26}, {x1 -> 8, x2 -> 5, x3 -> 11, 
  x4 -> 25}, {x1 -> 8, x2 -> 5, x3 -> 12, x4 -> 24}, {x1 -> 8, 
  x2 -> 5, x3 -> 13, x4 -> 23}, {x1 -> 8, x2 -> 5, x3 -> 14, 
  x4 -> 22}, {x1 -> 8, x2 -> 5, x3 -> 15, x4 -> 21}, {x1 -> 8, 
  x2 -> 5, x3 -> 16, x4 -> 20}, {x1 -> 8, x2 -> 5, x3 -> 17, 
  x4 -> 19}, {x1 -> 8, x2 -> 5, x3 -> 18, x4 -> 18}, {x1 -> 8, 
  x2 -> 5, x3 -> 19, x4 -> 17}, {x1 -> 8, x2 -> 5, x3 -> 20, 
  x4 -> 16}, {x1 -> 8, x2 -> 6, x3 -> 10, x4 -> 25}, {x1 -> 8, 
  x2 -> 6, x3 -> 11, x4 -> 24}, {x1 -> 8, x2 -> 6, x3 -> 12, 
  x4 -> 23}, {x1 -> 8, x2 -> 6, x3 -> 13, x4 -> 22}, {x1 -> 8, 
  x2 -> 6, x3 -> 14, x4 -> 21}, {x1 -> 8, x2 -> 6, x3 -> 15, 
  x4 -> 20}, {x1 -> 8, x2 -> 6, x3 -> 16, x4 -> 19}, {x1 -> 8, 
  x2 -> 6, x3 -> 17, x4 -> 18}, {x1 -> 8, x2 -> 6, x3 -> 18, 
  x4 -> 17}, {x1 -> 8, x2 -> 6, x3 -> 19, x4 -> 16}, {x1 -> 8, 
  x2 -> 6, x3 -> 20, x4 -> 15}, {x1 -> 8, x2 -> 7, x3 -> 10, 
  x4 -> 24}, {x1 -> 8, x2 -> 7, x3 -> 11, x4 -> 23}, {x1 -> 8, 
  x2 -> 7, x3 -> 12, x4 -> 22}, {x1 -> 8, x2 -> 7, x3 -> 13, 
  x4 -> 21}, {x1 -> 8, x2 -> 7, x3 -> 14, x4 -> 20}, {x1 -> 8, 
  x2 -> 7, x3 -> 15, x4 -> 19}, {x1 -> 8, x2 -> 7, x3 -> 16, 
  x4 -> 18}, {x1 -> 8, x2 -> 7, x3 -> 17, x4 -> 17}, {x1 -> 8, 
  x2 -> 7, x3 -> 18, x4 -> 16}, {x1 -> 8, x2 -> 7, x3 -> 19, 
  x4 -> 15}, {x1 -> 8, x2 -> 7, x3 -> 20, x4 -> 14}, {x1 -> 8, 
  x2 -> 8, x3 -> 10, x4 -> 23}, {x1 -> 8, x2 -> 8, x3 -> 11, 
  x4 -> 22}, {x1 -> 8, x2 -> 8, x3 -> 12, x4 -> 21}, {x1 -> 8, 
  x2 -> 8, x3 -> 13, x4 -> 20}, {x1 -> 8, x2 -> 8, x3 -> 14, 
  x4 -> 19}, {x1 -> 8, x2 -> 8, x3 -> 15, x4 -> 18}, {x1 -> 8, 
  x2 -> 8, x3 -> 16, x4 -> 17}, {x1 -> 8, x2 -> 8, x3 -> 17, 
  x4 -> 16}, {x1 -> 8, x2 -> 8, x3 -> 18, x4 -> 15}, {x1 -> 8, 
  x2 -> 8, x3 -> 19, x4 -> 14}, {x1 -> 8, x2 -> 8, x3 -> 20, 
  x4 -> 13}, {x1 -> 8, x2 -> 9, x3 -> 10, x4 -> 22}, {x1 -> 8, 
  x2 -> 9, x3 -> 11, x4 -> 21}, {x1 -> 8, x2 -> 9, x3 -> 12, 
  x4 -> 20}, {x1 -> 8, x2 -> 9, x3 -> 13, x4 -> 19}, {x1 -> 8, 
  x2 -> 9, x3 -> 14, x4 -> 18}, {x1 -> 8, x2 -> 9, x3 -> 15, 
  x4 -> 17}, {x1 -> 8, x2 -> 9, x3 -> 16, x4 -> 16}, {x1 -> 8, 
  x2 -> 9, x3 -> 17, x4 -> 15}, {x1 -> 8, x2 -> 9, x3 -> 18, 
  x4 -> 14}, {x1 -> 8, x2 -> 9, x3 -> 19, x4 -> 13}, {x1 -> 8, 
  x2 -> 9, x3 -> 20, x4 -> 12}}