rec.puzzles Archive

To write a googolplex raised to a googolplex, you write a 1 followed by how many zeros?

arithmetic/digits/zeros/googolplex.power New

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Problem

To write a googolplex raised to a googolplex, you write a 1 followed by
how many zeros?

A googol is a number written with a 1 followed by 100 zeros.  A
googolplex, I believe (?), is a googol raised to a googol.

-- Chad Moore <csm@preferred.com>
Show solution
This is really just mathematics instead of a puzzle but here goes.

googol^1  has 100 zeroes
googol^2  has 100*2 zeroes
googol^3  has 100*3 zeroes
 .
 .
 .
googol^googol  has 100*(10^100) = 10^102 zeroes

Thus a googolplex is 10^(10^102)

Similarly, googolplex^googolplex has (10^102)*[10^(10^102)]
= 10^[(10^102)+102] zeroes.

-- Glenn C. Rhoads <rhoads@paul.rutgers.edu>

[ Editor: the usual definition of a googolplex is 10^googol =
10^(10^100), a 1 followed by a googol zeros; the figures above follow
the poster's definition, googol^googol. ]