Solution to the Superlong Necklace Problem

Okay, lets reiterate what we know (we'll condense it somewhat).

Broken Necklace:

a) 1/3 of beads at lady's feet
b) 1/6 on bed.
c) 1/2 of what remained (and 1/2 of what remained thereafter then 1/2 again) six times in all, fell everywhere else.
d) 1,161 pearls still strung.

Let X be the total of all the pearls originally.

A third plus a sixth makes a half of X.  So, the following equation is generated:

1/2(1/2^6) X = 1161.  The amount in the parentheses is that mysterious amount from part 'c'.  The ^ is for exponents.

Simplifying we get:

(1/128)X = 1161

X = 148,608