Question 1137880: There are 6 red points labelled R1, R2, R3, R4, R5 and R6, and 6 green points labelled G1, G2, G3, G4, G5 and G6. Using straight lines, each red point is connected to at least one green point and each green point is connected to at least one red point. The number of green points connected to R1, R2, R3, R4 and R5 is 5, 4, 3, 2 and 2 respectively. The number of red points connected to G1, G2, G3, G4 and G5 is 4, 3, 2, 1 and 1 respectively. Find the number of red points connected to G6?
thank you!
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! 
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.
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