9466495947891649649
Analyzing the Sequence for Digit '4' Counts
The objective is to count the occurrences of the digit 4 within the sequence $9466495947891649649$. The counting is restricted by two conditions:
- The digit 4 should not be immediately preceded by the digit 6.
- The digit 4 should not be immediately followed by the digit 9.
Step-by-Step Condition Check
We will examine each instance of the digit 4 in the sequence $9466495947891649649$ to see if it meets both conditions:
- Index 1: The digit is 4. Preceded by $9$ (✓ Condition 1 met: not 6). Followed by $6$ (✓ Condition 2 met: not 9). --> Count this 4.
- Index 4: The digit is 4. Preceded by $6$ (✗ Condition 1 failed: is 6). --> Do not count this 4.
- Index 8: The digit is 4. Preceded by $9$ (✓ Condition 1 met: not 6). Followed by $7$ (✓ Condition 2 met: not 9). --> Count this 4.
- Index 14: The digit is 4. Preceded by $6$ (✗ Condition 1 failed: is 6). --> Do not count this 4.
- Index 17: The digit is 4. Preceded by $6$ (✗ Condition 1 failed: is 6). --> Do not count this 4.
Final Count Determination
By applying the rules to each occurrence of the digit 4:
- Two instances of 4 satisfy both conditions.
Therefore, the digit 4 appears 2 times in the sequence according to the specified rules.
Similar Questions
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Important Questions from Number Arrangement
Six friends A, B, C, D, E and F are sitting in two lines, facing the north. Three persons are sitting in each line. F is sitting in the middle. C is just behind B. D is to the immediate right of E. B is to the immediate left of F. Which three persons are sitting in the same line?
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Refer to the following series and answer the question (all numbers are single digit numbers only).
(Left) 1 2 6 5 6 8 1 5 8 6 9 8 3 3 5 8 9 4 7 8 (Right)
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If 1 is added to each odd digit and 2 is subtracted from each even digit in the number 3842675, how many digits will appear more than once in the new number thus formed?
