# A Magic Square with SETs

Imagine a 3 by 3 grid. Start with the SET card shown below and place it in the upper left corner of the grid. Use 8 more cards to fill in the grid such that every row, column and diagonal forms a SET.

Let’s review the rules of SET:

The game of SET is played with 81 cards. Each card has 4 features: shape, color, number, and shading. Each attribute comes in 3 forms, as follows:

Shape: ovals, squiggles, or diamonds;
Colors: red, green, or purple;
Number: one, two, or three (shapes on each card);

The object of the game is to find a SET, or 3 cards for which each characteristic is either the same on all three cards or different on all three cards.

For example, the following 3 cards are a SET .

Shape: all different
Colors: all different
Number: all different

These three cards also form a SET.

Shape: all different
Colors: all the same
Number: all the same

The following 3 cards are NOT a SET.

Shape: two are the same, one different
Colors: all different
Number: two are the same, one different
Shading: two are the same (striped), one different

Now finally, back to our question. Start with the given card and pick 8 other cards to fill in a 3 by 3 grid such that every row, column and diagonal forms a SET.

```Hint

One approach is to use only striped cards.```