Re: [piecepack] Mathrix review #2

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.

More thought on this.  You don't need 30 equations only 15 as you only
need to convert each pair one way.  Therefore I now break and completely
solve Mathrix!  Bru-HA-HA-HA-HA-HA (evil villan laugh).

ln(1) = 0
floor(ln(ln(2))) = 0
floor(ln(ln(3))) = 0
floor(ln(sqrt(4))) = 0
floor(ln(floor(sqrt(5))) = 0

floor(sqrt(2)) = 1
floor(sqrt(3)) = 1
floor(ln(4)) = 1
floor(ln(5)) = 1

ceil(sqrt(3)) = 2
sqrt(4) = 2
floor(sqrt(5) = 2

ceil(sqrt(sqrt(exp(4)))) = 3
ceil(sqrt(5) = 3

sqrt(4) = floor(sqrt(5))

If we outlaw floor and ceil it's much harder.