> 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