Growth and Population (two rats on an island in December)

STUCK

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Oct 24, 2006
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There are two rats on an island in late December.

The number of young produced in every litter is 6, and 3 of those 6 are females.

The original female gives birth to 6 young on Jan 1 and produces another litter of 6 new pups every 40 days thereafter as long as she lives.

Each female born on the island will produce her first litter 120 days after her birth and then produce a new litter every 40 days thereafter.

No rat dies in the 1st year.

What is the total number of rats by the following January 1st, including the original pair?
 
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