In trios of 3, there are 28 ways to connect all 8 Corner Colours to one another. Get the straight (and diagonal) on most of them, and you'll have colour covered on all sides . . .
3 = 8
Applying the rule of 'all or nothing' to each of our three element primary colours, we see how Cyan, Magenta, and Yellow can become 8 Corner Colours.
To review the 8 combinations, go see Lupe and treat yourself to some ice cream.
3 = 27
Applying the rule of 'only on half' and giving each of our three element primary colours three possible quantities (all, half, or nothing), we end up with 27 combos, adding 19 Connector Colours to our previous 8 Corners.
To review the 19 'only on half' combinations, call Ulysses and order some pizza.
THREE IN A ROW = 28?
With 27 Colour Basics cards (the 8 'whole' Corner Colour cards and the 19 'half-and-half' Connector Colour cards), every Corner can connect to every other Corner, in 28 different 'three-in-a-row' connections. That may have you stumped. With only 19 Connector Cards, how can we make 28 different connections? Here's how:
- twelve of the Connector Cards connect only one pair of corners. That's 12.
- six of the Connector Cards connect two pair of corners. That's another 12.
- one Connector Card connects four pairs of corners. That's 4 more.
12 + 12 + 4 = 28.
Let's take a closer look...
Twelve Connector Cards connect only one pair of corners.
These are straight connections, connecting Corners that are different by only one C, M, or Y primary element. For example, going from White to Cyan (adding only Cyan), or Cyan to Blue (adding only Magenta), or Blue to Black (adding only Yellow). In a straight connection, only one element changes, like going from an empty cone to one scoop, or a single scoop to a double, or a double scoop to a triple.
These scoop-by-scoop single element connections can work the other way too. In regular math, we know that the equation A + B = C can also be written as C - B = A. It's the same in Colour Math: C + M = B is the same as B - M = C. Or, in the case of grandpa eating his triple scoop ice cream...
Start with the 'all' of Black and take away Cyan, you're left with Red. Take away Magenta, you're left with Yellow. And take away Yellow, you're left with the 'nothing' of White.
Here are all 12 'Straight Threes':
The three straight connections at the top show White connecting to Cyan, Magenta, and Yellow: the 'single scoop' Hues as Tints. The six in the middle show the pure Hue-to-Hue connections: singles to doubles. The three at the bottom show Red, Green, and Blue connecting to Black: the 'double scoop' Hues as Shades.
Six Connector Cards do double duty and connect two pairs of corners, two 'scoops' at a time.
These are diagonal connections, connecting Corners that are different in two elemental ways. For example, going from 0 to 2, like White to Red (because White has 0 Cyan, 0 Magenta, and 0 Yellow and Red has 1 Magenta + 1 Yellow); or going from 1 to 3, like Cyan (a 'single scoop' Hue) to Black (a scoop of all three).
In each of these first six examples, we're adding two elements: in the top row, going from White to a 'double scoop' Hue, and in the bottom row, going from a 'single scoop' Hue to Black.
You can also flip the equation and see these as subtracting two elements, going from 'triple scoop' Black to 'single scoop' Cyan, Magenta, and Yellow; and going from 'double scoop' Blue, Red, and Green directly, diagonally, to White.
The other six diagonal connections use the same six Connector Cards, but cross diagonally in the opposite direction, adding and subtracting at the same time.
Here are all 12 'Diagonal Threes':
HALF: MIX OR AVERAGE?
Look at the first pair of connections, with the Connector being a Tint of Red. In one direction, that makes sense, this Tint being a 'half-and-half' mix of White and Red. But going the other direction, how can Yellow plus Magenta be a Tint of Red? Colour Math tells us M + Y = R, not R + W.
And look at the first new diagonal connection in the bottom row. Isn't the Hue between Green and Blue simply Cyan, not a Shade of Cyan?
Here's what's happening. Even though the Colour Squares on the Connector cards show a half of one Corner Colour and a half of another, the resulting Connector Colour isn't always a mix of these two 'halfs.' It's more of an average between them, which sometimes is, but isn't always, the same thing. More on that later.
Using what you learned about straight and diagonal connections, can you combine the twelve Straight Threes with the twelve Diagonal Threes to make six 3 x 3 grids of Nine? Think of the diagonal pairs as Xs in squares, and the straights as their edges. If you need any help, or want to check your answers, if you have the Colour Basics deck, you've had the answers all along. Two words: Cube Cards.
There's one Connector Card we haven't talked about yet, but it's the most important middleman of all. Best known as the go-between between Black and White, it's also the Connector for not just the other pairs of opposite Corners, but for all the Connector Cards too... a total of 13 pairs of opposite colours.