A diamon's price is ratio to square of its mass(not sure if it true in reality). If the diamon was cut to 3 smaller diamonds the ratio remain the same. Is the owner got more money or less , if he sold the diamond as a big one or cut it to three smaller ones?If it it true, that he will lost money if cut the diamond by three smaller one, in which case, the money lost it most?
A little suggestion: In my opinion, it is a lot easier for one to read and understand other's solutions if all of us use same variables refer to the same problem. So if you thing my suggestion is not violate your "free of choice" please use the following:
Let M be the mass of the big diamond, and a, b and c be the masses of the 3 smallers one after cut.
Let P be the price of M and x,y,z be prices of a, b, c respectively.
Then what was given is:
P/M^2 = x/a^2 = y/b^2 = z/c^2
find if: P > x + y + z *
and if * is true, find Max(P - (x + y + z) )
Please have fun.