*To*: piecepack@yahoogroups.com*Subject*: Re: [piecepack] Mathrix review #2*From*: "Mark A. Biggar" <mark.a.biggar@...>*Date*: Wed, 28 Jan 2004 00:59:11 -0800*In-reply-to*: <20040128071215.GA7491@...>*References*: <20040128071215.GA7491@...>*User-agent*: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.4) Gecko/20030624

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. -- mark@... mark.a.biggar@...