We can stack balls like in the picture below building a tetrahedron.
A tetrahedron with six layers is chosen. Each ball is assigned an integer number which is the sum of the numbers on the three adjacent balls in the layer below it. We only know the numbers on the balls at the three vertices of the bottom layer and they are 1, 2 and 3 respectively. When the number on top ball is divided by 5, what is the remainder?
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