11 modular 100 Fibonacci? Sounds Crazy!

Find the sum of all the Fibonacci numbers less than 1 billion which have their last 2 digits same in decimal representation.

Details and assumptions:

Fibonacci sequence is defined as \(F_0=0,F_1=1\) and for \(n\geq 2\), \(F_n=F_{n-1}+F_{n-2}\). Thus, the Fibonacci sequence is \(0,1,1,2,3,5,8,13,\ldots\).

  • 12344 has the last 2 digits same (each being 4), and 12345 does not have it's last 2 digits to be the same.

This problem is a part of the set Crazy Fibonacci

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