Game strategy.

The colorball puzzle is fun and not too difficult to solve, at least if you use the right strategy.
The 3×3 version is solvable by just trying, but the 4×4 version will take a long time in this way. On this page I will try to explain the way I use to solve this puzzle.
Let’s start with a 3×3 puzzle and later on I will use this technique on a 4×4 puzzle.
This is the puzzle:

There are nine pieces and nine different colors.
The first thing I would do is to find a piece with a color that has no matching color on another piece. Take piece nr 1, the orange on the right is unique, that is there is no other piece that has orange on the left!
Because this color is on the right side, it has to be placed on the board on the right side. It still could be on any row, but we start with placing it on the middle row:

Now we have to find another piece. Either on the top, bottom or left side of this piece.
On the left side there are 2 possibilities, nr 3 or nr 9.
On the top only nr 5 would fit. On the bottom there are 3 possibilities, 4, 7 or 9.
We take the one with the least possibilities, piece nr 5.

By placing piece nr 5 on top, it is clear that only piece nr 6 can be placed to the left of nr 5.

Now it is only a matter of completing the puzzle ( or not ? )

Now piece nr 9 must be placed below 6 and that piece nr 3 should be left of nr 6.
And now we are stuck, there is no piece that would fit below piece nr 3. Where did we go wrong?

Actually we did not do much wrong, we only have to backtrack to where we got multiple possibilities. In this case that is quite easy. All moves we made were mandatory, only the very first move, where we positioned the first piece in the middle row had multiple choices. We could move the first piece to the bottom row. But we would end up in a simular situation:

We would still be stuck.
So it is obvious that piece 1 should be on the top row. Now we can start filling the board again,

Now it is easy to finish.

Coming soon: Use this strategy for a 4×4 puzzle.