Question 1137880
{{{ highlight( 6 ) }}}

<pre>

Workout:

The short way:  there are 16 connections from red, and 11 connections 
from green.  The green metrics exclude G6, therefore, 16-11=5 connections 
must be coming from G6.  Since the red metrics don't include R6, one
more connection must go from R6 to G6, making the total number of 
connections to G6 equal to 6. 

I have to admit, I wouldn't have been as certain about this answer without
having first done the alternative solution below.

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Alternative method, which is more visual:

Starting with R1, connect to G1, G2, ..., G6 to satisfy the connection 
numbers for R1, taking care to AVOID connecting to G6 when possible.  
When stuck, revisit earlier R connections and move one of 
them to G6.   Repeat for R2, R3, ..., R6


     G1  G2  G3   G4   G5   G6
R1    1   1   1    1    1          (5)
R2    1   1   1              1     (4)
R3    1   1                  1     (3)
R4    1                      1     (2)
R5        
R6
     (4) (3) (2)  (1)  (1)


When attempting to make the two connections from R5 to two G's, we 
see there is no way to do that because only G6 is available and we need
to make TWO connections.  Revisit R1 and move the G5 connection to G6, that
frees up G5 for the 2nd connection from R5.  Also, note that R6 needs at 
least one connection to a G, and only G6 is possible while satisfying the
given conditions:  


     G1  G2  G3   G4   G5   G6     
R1    1   1   1    1         1     (5)
R2    1   1   1              1     (4)
R3    1   1                  1     (3)
R4    1                      1     (2)
R5                      1    1     (2) 
R6                           1     (1)
     (4) (3) (2)  (1)  (1)  [6]

[ This configuration has 17 connections to green, and 17 to red. ]


We see there must be 6 connections to G6 in order to satisfy the given 
conditions.