SET

Recall that a SET is a trio (TRES) of cards that for each of the FOUR characteristics, 

they are either all SAME, 

or they are all DIFFERENT.

The 3 cards that make a SET have to be different on at least one of the 4 characteristics. They can't be the same on all 4 characteristics. Otherwise they would be identical. Each card is unique. No repititions.

Here's a math/geometry way of finding a SET. It's sort of like playing tic tac toe, but on a bigger grid with 9 tic tac toe grids simultaneously.

And you can make a tic tac toe "winning line" (i.e. find a SET) by using all 9 tic tac toe grids. Don't restrict yourself to just one of those 9 tic tac toe grids.

So, in conclusion, there are at least 4 ways to find a SET:

1) You can find a SET by pattern recognition. This is sort of intuitive and kids usually find it naturally and easily, and look at you funny when you ask them to explain their thinking, like what can't you see it?

2) You can find a SET by verbal description. This is sort of how adults slowly talk themselves into verifying that they found a SET.

3) You can find a SET by using Base 3 math (3 cards make a SET if their Base 3 math modular addition results in 0000).

4) You can find a SET by sort of imagining (or using) those 9 tic tac toe grids.

ARRANGEMENT 1

ARRANGEMENT 2