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Read the following sequence and answer the question: (All numbers are single-digit numbers, and all calculations must be performed from left to right).
5 4 6 3 4 1 7 9 5 4 8 1 5 2 3 1 7 1 7 4 3 9 6 9 4 5 1 4 7
How many such pairs of digits are there, each of which has a perfect square immediately before it and an odd digit immediately after it?
Note: 1 is to be considered a perfect square.
5
6
3
1
5
Scan the sequence for triplets [Perfect Square - X - Odd Number], where Perfect Squares are 1, 4, 9 and 1 is explicitly defined as a perfect square.
Scan the sequence for triplets [Perfect Square - X - Odd Number], where Perfect Squares are 1, 4, 9 and 1 is explicitly defined as a perfect square.
Define criteria
We need to find triplets of numbers (A, B, C) where A is a perfect square (1, 4, 9), B is the number we are looking for (part of the pair), and C is an odd number (1, 3, 5, 7, 9).
Analyze the sequence
Sequence: 5, 4, 6, 3, 4, 1, 7, 9, 5, 4, 8, 1, 5, 2, 3, 1, 7, 1, 7, 4, 3, 9, 6, 9, 4, 5, 1, 4, 7. Scanning for triplets (Square, Any, Odd): (4,6,3), (4,1,7), (9,5,4)-No, (1,5,2)-No, (1,7,1), (1,7,4)-No, (9,6,9), (4,5,1), (4,7,X)-No. Let's list the valid pairs (the middle number) whose preceding number is a square and succeeding number is odd.
Identify valid triplets
B, C, and D are incorrect as the pattern analysis identifies exactly 5 instances of such pairs in the provided sequence.
A is correct because a thorough scan of the sequence identifies exactly 5 pairs that meet the criteria of having a perfect square before them and an odd number after them: (4,6,3), (4,1,7), (1,7,1), (9,6,9), and (4,5,1).
When counting occurrences in a sequence, mark the digits physically or mentally as you go to avoid double-counting or skipping elements.
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