Shuffle the main deck and place it somewhere where everyone can reach. Also within reach of everyone, make a space for the play area, with a pen or pencil making the line of a fraction. Near this, place the units cards, face up, in their three separate stacks. As you play, you will add "unit" cards to two rows, above and below the line. You should decide now which side is the top and which is the bottom. Players start out with no cards in their hands, but you need to pick "hidden cards" before you begin.
Each person draws a card from the main deck. If it is "Square", "Square Root", or "Clear", put it back into the deck and draw again. When you draw a legal card, put it face down in front of you. This is your "hidden card." You may not play it. If the combination of units in the play area ever matches your hidden card (it has to be right-side-up), you can flip up your hidden card and declare yourself the winner.
The game can be played by 2, 3, or 4 players. With four players, have two teams - sit across from your partner, and share a hidden card.
2. On your turn
Choose a first player by some method. Players take turns, going clockwise around the table. On each turn:
Draw one card from the top of the main deck.
Play any number of cards, one at a time.
Discard a card if necessary to reduce your hand to 3 cards. (You may never have more than three cards in your hand, unless it is your turn.)
When you play a card other than "Square", "Square Root", and "Clear", you may choose whether to play it right-side-up or upside-down. Whatever units are written on the card, take those unit cards from the stacks near the play area and add them to the play area on the appropriate side of the line. So if I play Force right-side-up, I add a kg and an m to the top row of the play area, and two s's to the bottom row. If I play it upside-down, I do the opposite.
Once you have played a card, you may need to "cancel". If one "unit" card appears both in the top row and in the bottom row of the play area, remove one of those cards from each row. Repeat this until no unit appears in both rows. So, (m s / s) becomes (m / ).
3. Special Cards
There are three special cards in the deck. These cards, rather than adding a specific set of units, do something to the units already in the play area. The "Clear" card clears all units out of the play area. The "Square" card doubles up every card in the play area. So, for every card in the play area, take one like it from the piles and add it to the same row of the play area. The "Square Root" card has the opposite effect from "Square" - it removes one card out of every pair. "Square Root" may only be played if all units in the play area are paired up.
4. Sample Game
Here's part of a sample game that displays how play works and what some of the strategy is like. In this game, there are two players. Russell's hidden card is Distance (m / 1), and Michael's is Energy (kg m2 / s2). It is Michael's turn, and the play area is blank. He draws a card, then plays two cards:
The first card makes him add an m to the top and an s to the bottom (m / s). The "Square" doubles these up, adding another m to the top and another s to the bottom (m m / s s). Micheal ends his turn.
Russell draws a card, and thinks he sees a way to win this turn. He plays three cards:
The card "Mass" adds a kg to the top and has no effect on the bottom (kg m m / s s). The card "Surface Tension", played upside-down, adds two s's to the top and a kg to the bottom (kg m m s s / s s kg). Then Russell has to cancel some cards. He removes a kg from both the top and the bottom, and two s's from both the top and the bottom (m m / 1). The "Square Root" then removes one of the remaining two m's, leaving the play area showing Distance, Russell's hidden card.
Unfortunately for Russell, Michael has already won. When Russell played "Mass", the play area was showing the unit "Energy". Therefore, Michael can flip up his card and announce that he has won. He can do this even if Russell starts adding the units from the "Surface Tension" before he realizes what has happened; all that is required for you to win is that your hidden card matched the units in the play area after some card was played. Russell should have played "Surface Tension" first, creating a unit not in the deck.