Tjoppen

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1. problem to solve

Sounds like homework... Just use ye olde product of modulus squares for aquiring the answer. If you're smart you only need to code addition/binary shift if the problem requires bignum.
2. Distance to bezier surface

(No school for four weeks, might have an error or two) You can also solve (u,v) for the ray starting at f(u,v) pointing in the direction of the normal at the same point, which crosses P This is because the line from the closest point to P is perpendicular to the surface. so f(u,v) + normal(f'(u,v))*t = P for some values of u, v and t. Probably more complicated then other suggested methods. Or not. Try it.
3. 64 bit 32.32 fixed point divide

Just brainstorming; __int64 c = a / b, //integer part d = a % b; //fraction * b result = (c << 32) + (((d << 31) / b) << 1); Something like that might work.. For instance: 3.0/2.0 = 1.5 a = 3<<32, b = 2<<32 c = 1 d = 1<<32 result = (1 << 32) (=1.0 fixed pt) + (((d << 31) (=1<<63) / (2<<32) (=1<<30)) << 1) (=0.1(base 2) fixed pt) result == (1<<32) + (1<<31) = 1.1(base 2) = 1.5(base 10) There are however precision issues. And it probably doesn't work with b > 2.0 Try experimenting with the expression A/B = (a+b)/(c+d) = a/(c+d) + b/(c+d) Where a and c are the integer part and b and d are the fractional part of A and B Possibly one could take the individual bits(ones only needed. 0/X = 0) of A, divide them by B and add them back together to form the result. I dunno, experiment.
4. dimensions in games

Only remember two, which are(IIRC): Quake: 1 unit = 1 inch, -16384 to 16383 Serious Sam: 1 unit = 1 meter, whatever a float(or was it double?) can hold I'd prefer the latter. Makes for easier use aswell since all constants in our physics lookup tables are metric.
5. zipping songs

Also you can create a solid archive with WinRAR which might shave off halv a percent or so..
6. Anti-Game Tampering Solutions?

Put the hash of the .exe at the end of the same .exe(also don't hash that last part). That way you don't get that conspicious "config.raw"-file in there.. When an inconsistency is noticed, don't just blurt out an error - let it wait for day or two so the cracker thinks it's okay and releases it. You can also put some functionality in dlls, strangely named in your archives. Encrypted of course. Even sneakier, watermark your encrypted dlls into picture data - perhaps the game logo itself which is displayed in the main menu. Your imagination's the limit!

Why not A* instead of Dijkstra's? Surely it makes more sense to use that for the "findings" of the different cases..
8. Deforming Objects

Idea: To simulate cracking, you could clip the cube with "random" planes and give the pieces velocity pointed away from the splitting plane Another thing could be CSG subtracting say an explosion sphere from the cube.
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