There are five cards lying on the 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 of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card?
Options:
A . 210
B . 210 × 33
C . 4 × 34
D . 42 × 33
Answer: Option C The remainder on the first card can be 0, 1, 2 or 3 i.e. 4 possibilities. The remainder of the number on the next card when divided by 4 can have 3 possible values (except the one occurred earlier). For each value on the card the remainder can have 3 possible values. The total number of possible sequences is: 4 × 34
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