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A B A C A A B A C A A B A C A ...... The letter appears times in the pattern. What is the greatest possible number of letters in the pattern?
Full solution
Q. A B A C A A B A C A A B A C A ...... The letter appears times in the pattern. What is the greatest possible number of letters in the pattern?
- Identify Pattern: The pattern is and we need to find the total length of the pattern if appears times.
- Pattern Repeats Every Characters: Notice the pattern repeats every characters (), and within this pattern, appears times.
- Calculate Full Patterns: Divide the total number of 's by the number of 's in the repeating pattern to find how many full patterns we have: full patterns and 's left over.
- Determine Remaining Characters: Each full pattern has characters, so full patterns have characters.
- Add Remaining Characters: For the remaining A's, we add the smallest number of characters needed to include them in the pattern. The sequence for A's is ＂ABACA＂, which adds characters.
- Calculate Total Length: Add the characters from the full patterns to the characters needed for the remaining A's: characters.
