a x b + c T R E E N E X (a + b) x c
```Three Number Expressions

This is a math card game for 2 to 4 players.  Materials needed are:
paper, pencil, and a deck of cards numbered from 0 to 9.  Calculators are
optional.  For the cards, one can use ordinary playing cards, counting the
10 or joker as a zero (0); or a special deck can be constructed from
tagboard or 3×5 file cards.

The basic objective is to create expressions of three numbers in
the form a × b + c or (a + b) × c.  When a player's expression is correctly
evaluated, the result is considered to be his/her score for that hand.

The rules for a three-player game will be used to describe the
general procedure.  Then other versions will follow naturally.

1.	Each player has paper and pencil for recording his/her results.

2.	The dealer deals two (2) cards to each placer face down.  Then
one card is placed in the center, also face down.  This is
called the common card.

3.	The player to the dealer's left turns his cards face up and
decides which operation to perform on the two numbers, addition
or multiplication.  The decision is then announced and the
expression is written on paper for all to see.  [Note: if addition
is selected, the values are written inside parentheses, (a + b).
Otherwise, the values are merely written in the a × b form.]

4.	The dealer and the other player now turn their cards face up.
They, however, must form their expressions using whichever
operation the first player did NOT use for his expression,
writing them on their papers in the manner described in the
note above.

5.	The common card's value is now revealed and utilized by all
players to complete their "Treenex" (Three Number Expression) in
the following way: (1) if addition was used for the first two
numbers, multiplication must be used with the third number; thus
forming an expression of the form (a + b) × c.  However, (2) if
multiplication was used first, then addition is now used to
complete the expression in the form of a × b + c.

6.	Each player computes the value of his/her expression.  Standard
order of operations are followed, namely, the value inside the
parentheses is done first for the expression (a + b) × c, followed
by the multipication.  Or multiplication is done first for the
a × b + c expression, followed by the addition.  (Each result may
be verified by the other players to avoid controversy.  Here
calculators may be used if the need is felt.)

7.	Scores are duely noted, and play passes to the 2nd hand.  This
time the third player makes the "first operation decision", thus
forcing his/her opponents to use the other operation in their
initial positions.  (Of course, for the 3rd hand, the dealer
takes his turn to make that "first operation decision".)  Play
proceeds as described above (#2-#6).  After the third hand, the
scores are totaled.  The player with the high score is declared
the winner.  Again calculators might be used for this.

VARIATIONS

The winner can also be declared to be the person who has the LOW
score, or even the MIDDLE score.  This must be agreed upon before play
begins, naturally.  This obviously chages the thinking strategies for
the player who makes the "first operation decision" in each hand.

Also the rules for the 3-player game can easily be adapted for 2
to 4 players.  First in this case, four hands should be played.  For 2
players, the "first operation decision" would be made on alternate turns;
for 4 players, each one would receive his/her own turn for that.  (And of
course, more hands could always be played to constitute one "Game".)

Next if the players understand negative numbers, subtraction could
be substituted for addition.  Also a larger deck of cards could be used,
or just put larger numbers on the cards [say, 10 to 19, for example].

As one can easily see, there are many possible variants to the
basic game.

tt(9/26/92)

```