I noticed a lack of mathematical games, in this forum, so here's one for people who enjoy working with numbers. (Personally, I love it, and have played this game on my own from time to time.)
The deal is that you create a mathematical expression, using four fours and any common mathematical operators, to create every integer from 0 to... Well, however far you can manage to go. In my own experience, I've seen these things go up into the hundreds.
Factorial: Factorial is written as a N (N being any number) with an exclamation point after it, and it is equal to the product of all integers between 1 and N, inclusive. So If you had 4!, that would be 4*3*2*1, or 24.
Exponentiation: This is just raising a number to the power of another number. But keep in mind you can only use fours, so you cannot raise anything to some random number such a 3, but you can raise a number to an expression involving only 4s. That is, if you did 4^(4*4), that's essentially 4^16. And, for anyone unaware, what that means is you multiply 16 4s together.
Square Root: In many versions of this game, sqr is not allowed, because it's essentially raising a number to 1/2, which is obviously not allowed. However, for the sake of simplicity, we'll call sqr a standard mathematical symbol in-and-of itself, and use it.
We probably won't need to go anywhere above there (not for quite a while, anyway). And remember, you cannot arbitrarily use numbers aside from 4. So to use !3, you'd have to write !(4-(4/4)), or whatever you can think of. And what I just used took up three of your four fours.
Gamma: Gamma is easier to explain. Here's the equation for it:
Y(X) = (X - 1)!
So:
Y(4) = (4 - 1)! = 3! = 6
Anyway. It was a large introduction, but most people can skim a large bit of it.
Only do one number at a time, and no double-posting unless there's a gap of 24 hours or more. And don't forget, we're going in order from 0 to infinity, so don't post any out-of-order. Like I say, I know firsthand that a few hundred are possible, at least, so if you can't figure one out, don't skip it. Feel free to ask questions if you want. (As in, every single post does not have to be the solution for the next number, if someone has a legitimate question to ask. But no chatting, for obvious reasons.)
