No Broken Eggs Puzzle

Jack is a farmer and owns some chickens. One day, he took a basket of fresh eggs to the market to sell.

The first person bought half of all the eggs in the basket and half an egg.

Then, the second person bought half of the remaining eggs and half an egg.

Later, the third person bought half of the remaining eggs and half an egg.

Finally, the fourth person bought half of the remaing eggs and half an egg.

Now Jack's basket is empty.

If no eggs were broken in the process, how many eggs did he originally have in his basket?

Birds in Garden Puzzle

Once upon a time, there was a garden somewhere in the world. In that garden, there were some birds on the ground and some birds on a tree.

The birds on the tree say to the birds on the ground that if one of you came to our tree, then our population will be double of yours.

Then the birds on the ground tell the birds on the tree that if one of you came to the ground, then our population will be equal to that of yours.

How many birds were on the ground and how many birds were on the tree?