what is the greatest number we can write by using the digit 2 four times ?

Answer 1

I'm guessing 2^2^22

* * * * *

Looking at some of the other answers, sorry, mine's bigger. :)

2^2^22 is 2^4194304. This number has over 1,260,000 digits. It's amusing all the negative votes I have (cool, I have a fan!), seeing as this number is much larger than other numbers being proposed. The only larger ones utilize factorials, and I think those have to be disallowed, since then just two 2s can make a number as big as you want - write it as 22!!!!!!!!!!!!!...

By the way, 2/0 is not a number, it is undefined. Infinity is not a number.

Answer 2

I also agree that it depends on what you mean by "write." You could write a number starting with four 2's, then followed by infinitely many 9's. If you can only use operations and the number 2, then I would raise 2 to the 22 power, and raise 2 to the power of this result; that is,

2 ^ (2 ^ 22) = 2 ^ 4194304 = a number too big for all but supercomputers

For comparison,
22 ^ 22 = a number with 30 places left of the decimal
2 ^ 222 = a number with 67 places left of the decimal
2 ^ (22 ^ 2) = 2 ^ 484 = a number with 146 places left of the decimal

As you can see, the key is to raise 2 to the greatest possible power.

Answer 3

(2+2)/(2-2) = INFINITY (anything divided by zero is simultaneously positive and negative infinity, ie +- 0-0, sorry I don't know how to type the symbol)

or 2/(2-2) x 2 = 2 x INFINITY (that's twice the infinity)

or 22! ^ 22! = tends to INFINITY

or 2222 (without anything else, no symbols)

or 22/22 = 1 (number one is always the greatest, do you want to be number one?)

or 22-2/2 = 21 (is the greatest number of card value to win in Blackjack)

or ...the answer is 2, the first time you write using the digit 2, you get 2 as greatest number, the second, third and 4th time is the same, 2 remains the greatest number

or there are multiple answers, because the person reading it thinks number 2 is the greatest (not largest, like we think our Dad is the greatest man on Earth), then 2 or 22 or 222 or 2222 are all greatest number of all, if the person thinks number 3, for example, is the greatest number, because his son's born on 3 March, then the answer is no such number, it's subject to taste

or no such number again because you cannot write using the digit 2 no matter for how many times, you need a pen, pencil, marker or something real

The ultimate answer is... depending on the surface you write the digit 2, the greatest (size) of the number you can write is the total area of the surface you can write on minus the area without ink

^_^ Merry Christmas... Paopao, you look great

Answer 4

2^(2^(2^2)) = 2^(2^4) = 2^ 16 = 65536

2^222 ≈ 6.74 X 10^66

2^2^22 = 2^4194304 ≈ 2.065 X 10^1262611

But what about 2^(2^22!) = 2^(2^1124000727777607680000)
≈ 2^( 1.78 X 10^338357934209204947673)
= a huuuuuuugggeeeeee number!!!!

And 2^(2^22!)! is even huger [if such a word exists {8<0 ]

Answer 5

Here, I am considering digit 2 is to be used only 4 times.

2 ^ (22 ^ 2) = 2 ^ 484 = a number with 146 places left of the decimal.

(OR ELSE : (2 ^ 484)^LARGEST NUMBER THAT IS ALMOST COUNTLESS)

Answer 6

2^2^2^2

Answer 7

It depends what operations are possible.

If you can use the Ackerman function as a standard operation, well it gets really huge. But under the normal rules of games like this, I'd first guess at

2^(2^(2^2))= 2^(2^4)= 2^16= a large number

Those other answers are better hunh...........

:-(

Answer 8

256

Answer 9

22^22

Answer 10

I suppose you mean using only 2's and the usual algebraic operations? how bout 2^222, that' s huge