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There are five cards lying on a table in one row. Five numbers from among $1$ to $100$ have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by $4$. The remainder when each ofthe five numbers is divided by $4$ is written down on another card, i.e., a sixth card, in that order. How many sequences can be written down on the sixth card?

  1. $2^23^3$
  2. $4(3)^4$
  3. $4^23^3$
  4. $4^23^4$
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