Four 4's

Post Reply New Topic

31 = (4! + 4)/4 + 4!

Congratulations!

32 = [√(4)]^(4/4 + 4)

Would this be valid (digital root)?

33 = 4! + dr(4!+4!+4!)

Right! The digital root of any positive integer is defined with the floor function, thus

dr(n) = n – 9*|(n–1)/9| where the pipes represent the floor function.

It is a mathematical function and it meets the criteria of the OP, so why not!

I see a lot of people using square roots. Does the square root function really meet those criteria? I'm asking this because the square root is really a number raised to the power of 1/2, so it has a 2 in it.

Well, in a context like this those criteria are not meant to be strict. I only wanted to rule out all sorts of ad hoc functions, as I indicated on page 1, bottom. Yes, the square root includes a 2 in it but because it is a long-time convention to camouflage it with the root symbol, it is all right. The above mentioned digital root function, too, is all right because it was not invented by any of us to serve just the purpose of this thread. The Dirac delta function would be welcomed but because δ(4,4) = 1 consumes two 4's it fares no better than 4/4 = 1.

And logarithms?

Incredible! There is a whole Wikipedia article on Four Fours! I swear I didn't know! This has been my private hobby who knows for how long. All I can say is that obviously I re-invented it for myself.

Now I need to breathe into a paper bag.

Well, onwards, then! With digital roots, it becomes a lot easier... and a lot cheesier.

34: 4! + 4 + 4 + √4
35: 4! +4 + dr(4x4)
36: 44 - 4 - 4 - This one was tough as hell ...
37: dr((4!)!) x 4 + (4/4)
38: dr((4!)!) x 4 + 4 - √4
39: dr((4!)!) x 4 + dr(4!/√4)
40 = (√4+√4)/√(4%)*√4 - Or, less dramatically: 44 - √4 - √4

I'm pretty sure that several of those could be done more elegantly than by using dr((4!)!), which yields a digital root of 9, but I *really* wanted to use a number larger than 6.2 x 10^22.

Now that you mentioned, Euler published several works when totally blind. His last words were "I die."

41: 4! + 4! - dr(4x4)
42: 44 - 4 +√4
43: 44 - (4/4)
44: 44 - 4 + 4
45: 44 + (4/4)
46: (4!+4!) - 4 + √4
47: (4!+4!) - (4/4)
48: (4!+4!) x (4/4)
49: (4!+4!) + (4/4)
50: (4!+4!) + 4 - √4

1/2 = 4/(4+4) so doing square roots is o.k.

ruveyn

Also any integer can be generated by 4's.

4 +....+4 - n times divided by 4 = n. So any integer n can be generated by 4's.

ruveyn