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Refer to the given series and answer the question that follows (all numbers are single-digit numbers only, and all counting is to be done from left to right).
How many such odd digits are there, each of which is immediately preceded by a perfect square and immediately followed by an odd digit? (Note: 1 will be considered as a perfect square.)
5
2
1
3
5
Scan the series for triplets: (Perfect Square) (Odd Digit) (Odd Digit). Remember: 1, 4, 9, 0 are squares (0 is usually excluded or treated as non-square in these puzzles, but note 1 and 4 and 9 are definitely squares; 1 is explicitly given as a square).
Scan the series for triplets: (Perfect Square) (Odd Digit) (Odd Digit). Remember: 1, 4, 9, 0 are squares (0 is usually excluded or treated as non-square in these puzzles, but note 1 and 4 and 9 are definitely squares; 1 is explicitly given as a square).
Define criteria
Target an Odd Digit (O) such that it is preceded by a Perfect Square (S) and followed by an Odd Digit (O). Pattern: S тЖТ O тЖТ O. Perfect squares in single digits: 1, 4, 9. (Note: 0 is not a perfect square).
Scan the series
Series: 9, 1, 1, 5, 7, 8, 0, 4, 5, 9, 9, 4, 6, 9, 4, 1, 6, 6, 8, 1, 4, 3, 5, 0, 2, 1, 9, 8, 6, 1. Triplets: (9,1,1) тЖТ 9 is square, 1 is odd, 1 is odd (Matches). (1,1,5) тЖТ 1 is square, 1 is odd, 5 is odd (Matches). (1,5,7) тЖТ 1 is square, 5 is odd, 7 is odd (Matches). (4,5,9) тЖТ 4 is square, 5 is odd, 9 is odd (Matches). (1,6,6) тЖТ No. (1,4,3) тЖТ No. (4,3,5) тЖТ 4 is square, 3 is odd, 5 is odd (Matches).
Verify count
Let's re-scan carefully: (9,1,1), (1,1,5), (1,5,7), (4,5,9), (4,3,5). That's 5 instances.
B, C, and D are incorrect because the correct count of the sequence [Perfect Square, Odd, Odd] in the provided string is 5.
A is correct because the sequence patterns identified are (9,1,1), (1,1,5), (1,5,7), (4,5,9), and (4,3,5).
Always verify if 0 or 1 is included in the set of squares specified by the question. In reasoning puzzles, '1' is almost always treated as a perfect square, as noted in the prompt.
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