# how many cells?

Tue Apr 16 15:20:58 EST 1996

```Mr. P.F. Linehan (plinehan at hgmp.mrc.ac.uk) wrote:
[skip]
: >  I challenged my kids to come up with something to
: > count that there might be a googol of.

: Isn't there a famous problem ("The Pagoda problem"?) whereby 64 successively
: smaller discs (with a hole in the middle) are placed on one of three pegs.
: The idea is then to move the sixty four discs to one of the other pegs
: but a larger peg cannot be placed over a smaller one. Legend has it that some
: monks started and they claim that it will be the end of the world by the
: time they finish. They are certainly right as even at one move a second
: it will take longer than the known age of the universe.

It takes (2^N)-1 moves to move N disks, so 2^64 is about 10^21,
and at pi*10^7 sec/yr, this is 3*10^13 yr--indeed safely more than the
age of the universe.

: How many pegs
: would require a gagool of moves. What is a gagool anyway (100 exp 100?)

Last one first.  A googol is 10^100.  It is also 2^330, so it
would take a stack of 330 disks to require a googol of moves (maybe 333
to be sure).
Yours,
Bill Tivol

```