Brain Teasers
Largest 2 Digit Number
What is the largest possible number you can write using only 2 digits?
Answer
9 to the power of 9Hide Answer Show Answer
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This is a great one!
0/1 is infinite
Opps 1/0 is infinite
If you are allow use notation like ^ (to the power of)
then what about
9! ^ 9!
then what about
9! ^ 9!
I'm too lazy to check on this but what about 99!?
I think the following two solutions are larger than any of the previous comments: (9!^9!)! or (99!)!. In fact one can do this forever by simpy adding more factorials and parenthetical: (((((99!)!)!)!)!)! and so on and so forth. The point is there is no definite solution.
The notation of ^ is used only because superscripts can't be shown in this format. I don't think it is meant as a license to use any symbol you want.
Gizzer is the winner!
And hey, I actually got it right!
And hey, I actually got it right!
good one
Also, 1/0 is not infinite, but is undefined. As the denominator approaches zero, the value approaches infinity, but it never "gets there".
What about infinity (a sideways to the infinity-th power?
* a sideways 8 (it automatically made a smiley)
The teaser does state "ONLY TWO DIGITS" which means 2 digits and nothing else therefore the answer should be 99.
yeah - if you write it out on pen and paper you don't write the ^ - only a 9 and another smaller 9 on the top area and a bit to the right...
The largest number that can be represented with two digits and no symbols is using tetration. Tetration is written the same as exponentiation except with the exponent written to the left of the number instead of to the right.
An alternative notation uses Knuth's up-arrow notation: 9↑↑9
This is equivalent to 9^9^9^9^9^9^9^9^9^9.
A googol is the number 10^100: a one followed by 100 zeros). The estimated number of elementary particles in the observable universe is around 10^81, or 19 orders of magnitude less than a googol. Assuming that spacetime is quantized (exists is discrete chucks, like pixels in a picture), these chunks would be about 1.6 x 10^-33 meters on a side. There would be about a googol quantized chunks of space in a square meter.
A googolplex is the number 10^10^100: a one followed by a googol zeros. This is a number so large that the universe is not large enough to even write the number, even using a single quark to represent each digit. The number of quantized chunks of space in the observable universe would be around a googol squared: (10^100)^2: a one followed by 200 zeros.
9↑↑9 is larger than a googolplex raised to the googolplex power. This is an unimaginably large number, beyond human comprehension. There is no physical description that can even approach providing any meaningful way to imagine a number this large.
An alternative notation uses Knuth's up-arrow notation: 9↑↑9
This is equivalent to 9^9^9^9^9^9^9^9^9^9.
A googol is the number 10^100: a one followed by 100 zeros). The estimated number of elementary particles in the observable universe is around 10^81, or 19 orders of magnitude less than a googol. Assuming that spacetime is quantized (exists is discrete chucks, like pixels in a picture), these chunks would be about 1.6 x 10^-33 meters on a side. There would be about a googol quantized chunks of space in a square meter.
A googolplex is the number 10^10^100: a one followed by a googol zeros. This is a number so large that the universe is not large enough to even write the number, even using a single quark to represent each digit. The number of quantized chunks of space in the observable universe would be around a googol squared: (10^100)^2: a one followed by 200 zeros.
9↑↑9 is larger than a googolplex raised to the googolplex power. This is an unimaginably large number, beyond human comprehension. There is no physical description that can even approach providing any meaningful way to imagine a number this large.
The largest possible number is to take the size of the universe, divide it by the size of the smallest measurable particle; count the number of combinations required to orgainise all of these particles through every possible position in the universe and then to assume that this has been done every smallest measurable instant of time since the universe began. What else is there to count?
{BTW infinity is not a number.}
Limited to 2 decimal digits with no other symbols, the largest representation of a number uses tetration. Both decimal digits would be 9 with one raised, similar to an exponent but on the left side of the base number.
The raised number may be referred to as a hyperpower or a superpower in the same manner as an exponent is often referred to as a power.
The raised number may be referred to as a hyperpower or a superpower in the same manner as an exponent is often referred to as a power.
A more correct answer to that I posted three years ago:
The standard notation for exponentiation is with the use of dextral superscription. That is, a number (or expression) is raised to the right of the base number (or expression). In ASCII notation this superscription is indicated with a carat symbol, with the superscripted power being to the right-side of the carat.
9 raised to the 9th power ( 9^9 ) is 387,420,489.
A standard notation for tetration is with the use of sinstral superscription. That is, a number (or expression) is raised to the left of the base number (or expression). In ASCII notation, this superscription is indicated with a double carat (^^) before the superscripted hyperpower to right-side of the carats.
9 tetrated to the 9th hyperpower ( 9^^9 ) in ASCII-exponential notation
is 9^(9^(9^(9^(9^(9^(9^(9^9))))))). This value far exeeds that of a googolplex [ 10^(10^(10^2)) ].
A standard notation for pentration is with the use of sinstral subscription.
That is, a number (or expression) is lowered to the left of the base number (or expression). In ASCII notation, the hyperpower is indicated with a triple carat (^^^) before the superscripted hyperpower to the right-side of the carats.
9 pentated to the 9th hyperpower ( 9^^^9 ) in ASCII-tetrational notation
is 9^^(9^^(9^^(9^^(9^^(9^^(9^^(9^^9))))))). [Note that the top of this 'power tower' is ( 9^^9 ),
the value of 9 tetrated to the 9th hyperpower, i.e., the ultimate value of 9^^^9 is more than galactically mind-bogglingly huge.]
The standard notation for exponentiation is with the use of dextral superscription. That is, a number (or expression) is raised to the right of the base number (or expression). In ASCII notation this superscription is indicated with a carat symbol, with the superscripted power being to the right-side of the carat.
9 raised to the 9th power ( 9^9 ) is 387,420,489.
A standard notation for tetration is with the use of sinstral superscription. That is, a number (or expression) is raised to the left of the base number (or expression). In ASCII notation, this superscription is indicated with a double carat (^^) before the superscripted hyperpower to right-side of the carats.
9 tetrated to the 9th hyperpower ( 9^^9 ) in ASCII-exponential notation
is 9^(9^(9^(9^(9^(9^(9^(9^9))))))). This value far exeeds that of a googolplex [ 10^(10^(10^2)) ].
A standard notation for pentration is with the use of sinstral subscription.
That is, a number (or expression) is lowered to the left of the base number (or expression). In ASCII notation, the hyperpower is indicated with a triple carat (^^^) before the superscripted hyperpower to the right-side of the carats.
9 pentated to the 9th hyperpower ( 9^^^9 ) in ASCII-tetrational notation
is 9^^(9^^(9^^(9^^(9^^(9^^(9^^(9^^9))))))). [Note that the top of this 'power tower' is ( 9^^9 ),
the value of 9 tetrated to the 9th hyperpower, i.e., the ultimate value of 9^^^9 is more than galactically mind-bogglingly huge.]
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