Balls and Baskets (It's Basketball!)

First let us arrange all the even spaces first by blue,then by yellow.Further to decrease the adjacent squares near yellow,we can arrange such squares with yellow and red.Further arranging remaining squares with green,we get an arrangement as given. Hence the green one is left out to get a matching arrangement.

If 1 yellow ball was left out, then there are 9 yellow and 7 blue balls to fill 15 even numbered baskets. If all 9 yellow balls occupy even numbered baskets then 1 blue ball is left and 15 odd places left out of which minimum 9 can’t be occupied by green which leaves 6 baskets for green. This arrangement is not possible.

If 8 yellow and 7 blue balls occupy even numbered baskets and 1 yellow ball is placed in between 2 yellow balls then green will have (14 - 7 =) 7 baskets left, which is not possible.

Considering different cases (10 yellow balls in odd numbered baskets / 9 yellow balls in odd numbered baskets and 1 yellow ball in between 2 other yellow balls), the only case possible is 8 yellow and 7 blue balls occupying odd numbered baskets - remaining 2 yellow will occupy numbered baskets in between 2 yellow balls, green can occupy (15 - 8=) 7 baskets and 1 green is left out .

So the left out ball is green.

First I filled all the even places, as said by the question as shown in figure.

Now while filling green balls, which obviously I will start from first basket, I will face a problem, the problem is that, only 5 green ball can be used because green cannot be adjacent to yellow, so I replaced two yellow balls from 12th and 14th position with blue balls and green balls are filled in 11th and13th position. Red balls were filled from the back from the 29th to 19th position

And finally, one Green ball was left.

We see that all the blue and yellow balls occupy alternate spaces. Suppose all the 7 blue balls are placed first before the yellow ones. Then we have baskets 2, 4, 6....all the way until 14 occupied by blue balls. Baskets 16, 18, 20....all the way until 30 will be occupied by yellow balls. The green balls obviously cannot be in baskets 15, 17, 19.....29 as they would be adjacent to at least one yellow ball. So they can only occupy baskets 1 to 13. But this only accounts for 7 green balls. Since the 8th green ball cannot occupy any of the remaining baskets, it follows that THAT particular $\boxed{green}$ ball is the one left out.