# MathrixTextVersion

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```Title: Mathrix, The
Version Number: 1.0.0
Version Date: January 21, 2004
Number of Players: 1
Duration: Approximately 10 minutes
Equipment Needed: one standard piecepack (and if desired, a clock or timer)

The MathrixAn abstract piecepack solitaire for the mathematically inclined
SetupArrange any six tiles face-down in a two tile by three tile rectangle to
create a four space by six space rectangular grid.Shake all twenty four coins, then
without peeking at their values, place one coin face-down onto each of the twenty
fourgrid spaces. Finally, flip all of the coins face-up, and adjust their facings
so the values are easily readable. Set the rest ofthe piecepack aside. One of the
trillions of possible setups is shown below.

4 @   @ µ ? ?
3   µ ? ? ? ?
2 ? ? ? ? ? @
1 µ µ @   ?
a b c d e f
Goal & PlayRemove all but one coin by formulating mathematical equations using
strings of coins. The coins that make up theseequations must be orthogonally
adjacent to one another (no gaps), but may be read in any of the four cardinal
directions:left–right, right–left, up–down or down–up. Null coins have a value of
zero, and ace coins have a value of one. Once anequation has been formulated,
remove any one coin from the string that made up that equation (your choice). For
example, in the above diagram, starting at space d2 and reading down–up: 2 + 2 = 4.
With that equation, you couldchoose to remove any one of the three coins at d2, d3
or d4.
Repeat until only one coin remains (in which case you win) or until there are two
or more coins remaining, none of whichcan be removed (in which case you lose).
After learning the basics and winning a few games, keep track of your besttime!
Note: Each equation must, in fact, be an equation. In other words, exactly one of
the operators must be an equal sign.
Inequalities are not allowed because they would trivialize the game with operations
such as 4 < 5 and 3   2. Likewise,operations which introduce variables (including
most algebraic and calculus operations) are not allowed because theywould make the
game too easy. Almost anything else is legal, as can be seen in the sample game.
Use good judgement;if it feels like cheating, it probably is.
Strategy Tips1. Check to see if your setup is solvable. Most setups have a
solution, but some are less obvious than others. Look
for any two adjacent coins of equal value, a four adjacent to a two, or a string of
any length ending in zero thenone. If any of these are present, chances are very
good that your setup can be solved.2. Start by deciding where you want to end. The
strings listed in the previous strategy tip are usually good places toend the game,
so try to save them for last. The puzzle is figuring out how to get there.3. Stay
connected. Removing coins from the periphery is usually a good tactic. This reduces
the likelihood of coins
becoming stranded. Coins at the corners and edges have fewer connections, so they
are harder to remove laterin the game. Similarly, leaving holes in the middle of
the board can make the ending much more difficult.4. Consider the consequences of
every move. Once a coin is removed, it can no longer be used to form other

equations. Formulating equations is very easy at first, but it gets progressively
more difficult as fewer coinsremain. Try to delay removing coins that reduce your
choices for subsequent moves.5. Don’t use a calculator. While using a calculator is
allowed, once you start playing against time, thinking through
the equations in your head will be much faster than pressing buttons.
Annotated Sample GameLooking at the sample setup, there are several adjacent pairs
of coins having equal values. There are also several zerosnext to ones and a couple
of fours next to twos, so a solution should exist. In fact, many solutions do
exist, but only oneis presented here. Following the strategy tips, the 2,0,1 at
a2,a3,a4 appears to be a good place to end. Ending thererequires starting somewhere
else, and the periphery is usually the best place.
At this point, you might want to construct the sample setup with your own piecepack
and go through these steps to get afeel for how the process works. Each equation in
the sample game is followed with the location of the removed pieceenclosed by
square brackets. If you are following along, remove the indicated coins as you come
to them. By examiningthe neighborhood around the removed coin, you can find the
strings of coins that generate each equation.
The simplest possible equation is the identity equation, which is just one number
equal to another such as 4 = 4 [a1].There are several identity equations available
in the sample setup, such as 5 = 5 [f4]. While they are easy to find,
savingidentity equations for later in the game is usually prudent. The next
equation type is the arithmetic relationship using oneor more of the four basic
operators: addition, subtraction, multiplication and division. Many equations of
this type arereadily available in the sample setup, such as 3 + 0 + 1 = 4 [b1], 5 -
4 = 1 [e4] and 4 ÷ 2 = 2 [d4]. Making a positivequantity negative by preceding it
with a minus sign is allowed, as is taking the absolute value to make a negative
quantitypositive. The well-known “My Dear Aunt Sally” priority sequence
(multiplication and division before addition andsubtraction) applies, but priority
may be reassigned by using parentheses, such as 2 + ((2 - 5) ÷ (-2 + 5)) = 1 [f2].
Next upare the series and transcendental functions such as raising numbers to
powers, roots, factorials, logarithms andtrigonometric functions. These are most
useful when the number of coins begins to dwindle in the end game. Also notethe
special relationship that any number raised to the zeroth power equals one, so (0 +
3)^0 = 1 [f1]. The sequence 3^0 =1 [e1], cos(0) = 1 [c1] and 2 - 2 = 0 [d1] clears
the first rank. The 3 coin at f3 should be removed before it gets stranded,and 3 =
3 [f3] accomplishes this nicely. As with arithmetic operators, transcendental
functions may be combined, so morecomplicated equations such as 3 × 2^3 = 4! [e3]
are also legal. Remember, any mathematical operations which do notintroduce
variables or differential terms are fine to use, but complicated equations are
rarely (if ever) required. Onepossible example is c(5,2) = p(5,2) ÷ 2! [e2], which
employs probability functions.
If you have been following along so far, you should have a fairly good grasp of how
things work. One possible sequenceto finish the puzzle is: 2 = 2 [d2], 2 = 3! - 4
[d3], 5 - 3! = -1 [c2], alog(0) - 4 = -3 [c3], %4 = 2 [b3], 2 = 2 [b2], 1 + 0 = 1
[c4],acos(1) = 0 [b4], 2^0 = 1 [a2], and finally cosh(0) = 1 [a3].
CreditsProofreading: Amanda J.-L. RodefferPlay Testing: Jonathan Dietrich, Marty
Hale-Evans, Ron Hale-Evans, David Whitcher, Matt Worden

Revision History0.0.1, September 15, 2003 initial concept, title, headers, setup,
goal & play, strategy tips, revision history, license0.0.2?, September 16, 2003
edited piecepack terminology, diagrams, examples, annotated sample game0.1.0?,
September 17, 2003 style editing, credits, updated examples, first external play
test version0.1.1?, October 27, 2003 changed title, contest version1.0.0, January