Custom Search
by: Erik Oosterwal
|
Custom Search
|
1111 = 285311670611
2222 = Some number
with a million digits in it.
There is another less well known mathematical operation called tetration,
also called iterated exponentiation or hyperpower, which takes exponentiation
to the next level. Just like 1111 is shorthand for multiplying
11 by itself 11 times
(11•11•11•11•11•11•11•11•11•11•11),
1111 is shorthand for
11^(11^(11^(11^(11^(11^(11^(11^(11^(1111))))))))). My calculator
is capable of handling numbers up to 1•10500-1, and it blew
up after the second iteration of exponentiation. Since googol is
1•10100 and googolplex is
1•10^(1•10100), you can just imagine how big of a number
1111 is.
I can't wrap my head around a number that big and
2222 is multiples
of magnitudes larger than that. Those are some really, really, really
big numbers.
Of course we could get even more silly and bring up a couple of other lesser
known operations called Pentation and Hexation. Just like Multiplication
is a repeated addition, Exponentiation is a repeated multiplication, and
Tetration is repeated Exponentiation, Pentation is defined as repeated Tetration
and Hexation is defined as repeated Pentation. At this point the numbers
get so humongously large that they stop having any real useful purpose.
Incidentally, you can write the various math methods like this:
| Multiplication: | x*y, which means x added to itself y times. |
| Exponentiation: | x**y, which means x multiplied to itself y times. |
| Tetration: | x***y, which means x exponentiated to itself y times. |
| Pentation: | x****y, which means x tetrated to itself y times. |
| Hexation: | x*****y, which means x pentated to itself y times. |
See all the brain teasers on The Puzzle Page.
Get daily puzzles in your RSS reader at The Puzzle Page Blog Site.
Looking for answers to computer programming problems?
Read what's going on in the Computer Science 101 classroom.