The Four 4's Game

[Nervous Rex]

I'm going to create a few "recreational math" threads, to see if anyone's interested. This is the first.

Starting at 0 create a formula that produces each integer.
Use exactly four 4's (no more, no less) and no other digits.
You may use any math operation you want - add, subtract, multiply, divide, powers, roots, factorial, ceiling, floor, etc.

For example, you can use √, because writing it doesn't require any extra digits, but you can't use ∛, because it requires a 3.

Here are a few to start us off:
0 = 4 - 4 + 4 - 4
1 = 4 * 4 / (4 * 4)
2 = 4 * 4 / (4 + 4)

Edit:
Here's a Wikipedia article that lists some of the math operations used in the Four 4's game: Four fours - Wikipedia

 

[tree]

That reminds me of a game I have.
S'MATH Game, Irwin Toy, 028295 - Rainbow Resource

I don't think I can play the game in this thread.

 

[Vinca]

0 = 4 - 4 + 4 - 4

 

[Jeremiah]

3 = (4 * 4 - 4) / 4

 

[Vinca]

4 = (4 - 4) + √4 + √4

 

[Jeremiah]

5 = √4 + √4 + 4 / 4

 

[Vinca]

6 = (4 + 4 + 4) / √4

 

[Nervous Rex]

7 = 4 + 4 - 4/4

 

[FreeDiver]

8 = 4 + 4 - 4 + 4

 

[FreeDiver]

9 = 4 + 4 + 4/4

 

[FreeDiver]

10 = 4 + √4 + √4 + √4

 

[Nervous Rex]

11 = 4! / ((√4)!) - 4/4

When I played this game on paper by myself, I hit a wall and was completely stumped by one number. I wish I could remember what number that was.

 

[Vinca]

12 = (4 * 4) - ( square root of 4 + square root of 4)

(sorry about words instead of square root symbol...cant find it on my mobile phone)

 

[Vinca]

11 = 4! / ((√4)!) - 4/4

What do the exclamation marks represent?

 

[Crossbreed]

What do the exclamation marks represent?

Factorial. 4! = 4 x 3 x 2 x 1

 

[Vinca]

Factorial. 4! = 4 x 3 x 2 x 1

Ahhh! I never new that!! Thanks for explaining

 

[Crossbreed]

((√4)!)

That factorial is redundant.

 

[Crossbreed]

12 = (4 x 4!)/(4 x √4)

 

[Nervous Rex]

That factorial is redundant.

Oh, goodness. You're right. I use larger factorials regularly at work, so it didn't even occur to me to simplify.

 

[FreeDiver]

Factorial. 4! = 4 x 3 x 2 x 1

I never knew that ether as well. In programming, the exclamation mark means to "invert" or "NOT" a boolean operation.