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In the series: 5 4 2 8 3 6 4 9 2 5 7 4 8 3 6 1 4 2 9, how many digits are there which are immediately preceded by an even digit and immediately followed by an odd digit?
2
3
4
5
3
Scan for sequences of (Even, Digit, Odd) by placing your finger on the series and marking only the triplets that fit the Even-X-Odd criteria.
Scan for sequences of (Even, Digit, Odd) by placing your finger on the series and marking only the triplets that fit the Even-X-Odd criteria.
Analyze the sequence
The series is: 5, 4, 2, 8, 3, 6, 4, 9, 2, 5, 7, 4, 8, 3, 6, 1, 4, 2, 9. We need to identify triplets (X, Y, Z) where X is even, Z is odd, and Y is the digit being counted.
Mapping the triplets
Checking each Even digit X: (4,2,8), (2,8,3), (8,3,6), (6,4,9), (4,9,2), (2,5,7), (4,8,3), (8,3,6), (6,1,4), (4,2,9). Finding Even-X-Odd: 1) (4,2,8) no, 2) (8,3,6) yes, 3) (6,4,9) yes, 4) (4,9,2) no, 5) (2,5,7) no, 6) (4,8,3) yes, 7) (8,3,6) no, 8) (6,1,4) no, 9) (4,2,9) yes. Wait, let us re-verify: 1) 4-2-8 (E-E-E), 2) 8-3-6 (E-O-E), 3) 6-4-9 (E-E-O), 4) 4-9-2 (E-O-E), 5) 2-5-7 (E-O-O), 6) 4-8-3 (E-E-O), 7) 8-3-6 (E-O-E), 8) 6-1-4 (E-O-E), 9) 4-2-9 (E-E-O). Actually, checking triplets (E, ?, O): (6,4,9), (4,8,3), (4,2,9).
Final Count Verification
The triplets meeting the (Even, Digit, Odd) condition are: 1) 6,4,9 (Preceded by 6-even, followed by 9-odd), 2) 4,8,3 (Preceded by 4-even, followed by 3-odd), 3) 4,2,9 (Preceded by 4-even, followed by 9-odd). Total count is 3.
A: 2 is incorrect as the third valid triplet (4,2,9) is missed. C: 4 is incorrect as it overcounts by including triplets that end in even digits. D: 5 is incorrect as it assumes too many patterns without checking the Even-Odd constraint strictly.
B is correct because there are exactly three digits (4, 8, and 2) that are preceded by an even digit and followed by an odd digit.
When searching for patterns in long strings, always break the sequence into triplets immediately to avoid overlapping errors.
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