A 55-sided fair dice has an integer from 1 to 10 written on each face. Each of the numbers $$i = 1 \text{ to }10$$ is used $$i$$ times for a total of 55 numbers.

What is the expected number of times the die needs to be rolled so that every number has appeared at least once (to 2 decimal places)?


Note: This problem might require computational aids.

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