What is the largest number you can make with 3 one-digit numbers?

You've no doubt heard this one before. The answer you all know and love is 9 ^ 9 ^ 9, or some 369-million digit number that appears in Pi somewhere but no one cares to memorize.

Here are a few rules to that game:

1. The number must be less than infinity.
2. You cannot use unary operators. (Unary operators are operators that only require one argument to work, such as factorials. 1 + 2 = 3 is a binary operator, since it has two arguments, 1 and 2.)
3. If you use an iterated binary operator (one that is recursive, like 3^^3 which equals 3 ^ 3 ^ 3 or 3 ^ 27 or 7625597484987), you must define the number of times that the function or operator is iterated.
4. You may combine digits to form larger numbers. (999 is allowed, for example.)

Even abiding these rules, one can make much larger numbers than 9^9^9 using only fours, for example 4^^^^4 (4 arrows). This equals 4^^^4^^^4^^^4, which in turn equals 4^^^4^^^(4^^4^^4^^4), which equals 4^^^4^^^(4^^4^^(4^4^4^4)), and so on. It is truly a very large number, much more than 369 million digits.

Here is the first question of this "big numbers contest": What is the largest number you can make with four one-digit numbers?

Just as a note, this thread could possibly become considered spam... I would be careful.... the moderators/admin may consider it as spam if people are simply just listing numbers over and over... maybe if the posters explained how they got an answer... something along those lines may help.

Well, I don't intend for it to become spam, so yes, people will have to explain how they got their numbers. As a side note, you cannot repeat a number once it has already been said.

hmm

3^6x4^5

hehe very simple to begin with... 3 times 3, 6 times. 4 times 4, 5 times. both timesed by each other to form the product

so it would equal:

3 x 3 x 3 x 3 x 3 x 3 x 4 x 4 x 4 x 4 x 4

If my calculator is correct, that equals 2,239,488!

This post has been edited by A200: Feb 10 2008, 04:56 AM

Well, that's good, but how about this: 4^6x5^7?

That equals 4*4*4*4*4*4*5*5*5*5*5*5*5, or 320,000,000.

Keep going...

Are we allowed to use infinity in our equation as long as the final answer doesn't come out to infinity? If so I will have another equation, but uh if my calculation is correct this should be the biggest one so far...

Int(0,8)[x^9dx]=348,678,440

Thats:
=348,678,440
For those who can't read my text notation.

This post has been edited by alex7h3pr0gr4m3r: Feb 21 2008, 01:29 AM

Well, using four one-digit numbers I went straight for 9^9^9^9. That is big. So big, in fact, that not only did it crash Abakus trying to calculate it, but Google also failed. But trust me, that is pretty big.

Then of course you could go for 9^(9^^^^^^^^^9) (9 arrows). That uses four 9s (including the one to specify the number of times I iterate the power) and is also fairly large. Feel free to try to calculate that one.



I make the answer to your integral 107,374,182.4
The integral of x^9 is (x^10)/10. Putting numeric values in, you get (8^10)/10 - (0^10)/10, which is 107,374,182.4

Arghh I integrated correctly, but my arithmetic was wrong >.< Now I'm embarrassed. I shall come back with a better integral. By the way I thought we were only able to use 3 single digit numbers rvalkass...

Bah, I do that often enough. I can calculate circular motion, do loads of weird calculus but I can't add up



I thought it was four...