CEMC Cayley, 2005

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

The non-negative difference between two numbers $a$ and $b$ is $a - b$ or $b - a$ , whichever is greater than or equal to 0. For example, the non-negative difference between 24 and 64 is 40. In the sequence $88, 24, 64, 40, 24, \ldots$ , each number after the second is obtained by finding the non-negative difference between the previous 2 numbers. The sum of the first 100 numbers in this sequence is

(A) $496$ (B) $760$ (C) $752$ (D) $776$ (E) $405$

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