Challenge Try to solve this

There are 15 Blue Jays and 14 Orioles that wish to rest on the branches of three older trees. Each of the trees will have at least 4 Blue Jays and 2 Orioles. However, no tree may have more Orioles than Blue Jays in its branches. Determine the largest number of birds that can be in one tree.

This is how I would "think through" the problem.

Each tree will have at least  4  Blue Jays and  2  Orioles.

Let's go ahead and "put"  4  Blue Jays and  2  Orioles in each tree.

1^st tree:  4, 2          2^nd tree:  4, 2          3^rd tree:  4, 2          remaining:  3, 8

Now let's try to put as many of the remaining birds in the first tree as we can.

Let's put the rest of the Blue Jays in the first tree.

1^st tree:  7, 2          2^nd tree:  4, 2          3^rd tree:  4, 2          remaining:  0, 8

Now...no tree may have more Orioles than Blue Jays, so the maximum number of remaining Orioles that we can put in the first tree is  5  .

1^st tree:  7, 7          2^nd tree:  4, 2          3^rd tree:  4, 2          remaining:  0, 3

And it doesn't matter how we distribute the remaining Orioles.

The largest number of birds that can be in one tree is  14 .

There are 15 Blue Jays and 14 Orioles that wish to rest on the branches of three older trees. Each of the trees will have at least 4 Blue Jays and 2 Orioles. However, no tree may have more Orioles than Blue Jays in its branches. Determine the largest number of birds that can be in one tree.

Put   4 Jays  and 4 Orioles in each tree

So......we have   used 24  and there are 5 left  -  3 Jays and 2 Orioles

Put the 3 Jays in each of the trees   and 2 Orioles in any of  two trees

So....we will  have

5 Jays - 5 Orioles      5 Jays - 5 Orioles         5 Jays - 4 Orioles

Take   1 Jay and 1 Oriole from each of the last two trees and put them in the first tree

So we have this  arrangement

7Jays - 7 Orioles       4 Jays - 4 Orioles           4 Jays - 3 Orioles

Each tree has at least 4 Jays and  2 Orioles....and no tree contains more Orioles than Jays

And I agree with hectictar.....14 is the greatest number in any tree  !!!