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In the series: 1 3 5 2 4 6 7 9 1 8 3 5 2 4 6 2 8 5, how many odd digits are there, each preceded by an odd digit and followed by an even digit?
3
4
2
5
3
Quick Trick: Scan the sequence for odd digits (1, 3, 5, 7, 9) and look for the specific O-O-E (Odd-Odd-Even) triplet pattern.
Scan the sequence for odd digits (1, 3, 5, 7, 9) and look for the specific O-O-E (Odd-Odd-Even) triplet pattern.
Analyze the series
Given series: 1, 3, 5, 2, 4, 6, 7, 9, 1, 8, 3, 5, 2, 4, 6, 2, 8, 5. We need to identify an odd digit (O) that is preceded by an odd digit (O) and followed by an even digit (E). The target pattern is O-O-E.
Scanning for O-O-E triplets
Evaluating triplets sequentially: (1,3,5) тЖТ O,O,O (No); (3,5,2) тЖТ O,O,E (Yes, 5 is the target); (5,2,4) тЖТ O,E,E (No); (2,4,6) тЖТ E,E,E (No); (4,6,7) тЖТ E,E,O (No); (6,7,9) тЖТ E,O,O (No); (7,9,1) тЖТ O,O,O (No); (9,1,8) тЖТ O,O,E (Yes, 1 is the target); (1,8,3) тЖТ O,E,O (No); (8,3,5) тЖТ E,O,O (No); (3,5,2) тЖТ O,O,E (Yes, 5 is the target); (5,2,4) тЖТ O,E,E (No); (2,4,6) тЖТ E,E,E (No); (4,6,2) тЖТ E,E,E (No); (6,2,8) тЖТ E,E,E (No); (2,8,5) тЖТ E,E,O (No).
Consolidating the count
The triplets matching the pattern O-O-E are: (3,5,2) with middle 5, (9,1,8) with middle 1, and (3,5,2) with middle 5. Total count = 3.
B: 4 is incorrect as there are no other instances matching the O-O-E pattern. C: 2 is incorrect because it misses the third occurrence of the pattern. D: 5 is incorrect as it significantly overcounts the valid sequences present.
A is correct because there are exactly 3 instances in the sequence where an odd digit is preceded by an odd digit and followed by an even digit: the 5 in (3,5,2), the 1 in (9,1,8), and the 5 in (3,5,2).
When counting specific patterns in a long string, always work in triplets and mark them off to avoid skipping or double-counting elements.