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Re: [piecepack] Mathrix review #2



Mark A. Biggar wrote:

Ron Hale-Evans wrote:

 > I have a reservation about the game that is itself a puzzle of sorts.
 > It seems that some numbers in Mathrix can be treated as completely
 > identical to other numbers.  For example, 4 can always be treated as
 > equivalent to 2 when necessary, because sqrt(4)=2.  Similarly, a null
 > coin can always be treated as an ace coin as well, because cos(0)=1.
 > It seems to me that a 6x6 "mathrix" of such equations (leaving out the
 > cases 0=0, 1=1, etc., thus 30 equations in all) would render Mathrix
 > trivial, since you could always remove any coin from the board.  Can
 > such a table be constructed?  How abstruse would the math have to be
 > to show 4 can be converted to 5?  I'm interested to hear opinions on
 > this.  Barring the creation of such a table, of even most of one, by
 > piecepacking spoilsports :), Mathrix is plenty fun.
 >
 > By the way, I was able to get the coins in my first game down to the
 > following 3:
 >
 > 1 2 0
 >
 > I could take one further coin away by treating this as the equation
 > 1=2-cos(0), but that would leave either '1 2' or '2 0'. Removing the
 > '2' coin would be suicidal, because the '1' and the '0' coins would no
 > longer be adjacent and couldn't be used to form an equation.  Can
 > anyone create equations for '1 2' or '2 0'?  I couldn't find one, even
 > after breaking out my scientific calculator.

How about floor(sqrt(2)) = 1

floor and ceiling along with sqrt lets you change 5 into 2 or 3, 3 into
1 or 2.  Along with exp, you can use floor and ceiling to turn 0 into 1,
2 into 7 or 8, 3 into 20 or 21, 4 into 54 or 55 and 5 into 148 or 149.
Throw in sqrt as well to get a whole bunch of other numbers.

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