Discussion
Consider the following sequence of numbers:
6 9 2 2 2 6 8 9 1 3 7 5 2 6 7 6 7 7 5 2 9 1 6 4 6 3 9 8.
How many odd numbers are followed by another odd number in the sequence?
Answer: C
8 odd numbers are followed by another odd number.
Walk through the sequence 6 9 2 2 2 6 8 9 1 3 7 5 2 6 7 6 7 7 5 2 9 1 6 4 6 3 9 8 and mark each adjacent odd-odd pair:
- 9 1, 1 3, 3 7, 7 5 (four pairs in the run 9 1 3 7 5)
- 7 7, 7 5 (two pairs in the run 7 7 5)
- 9 1 (one pair)
- 3 9 (one pair)
That is 4 + 2 + 1 + 1 = 8. A run of k consecutive odd numbers contributes k − 1 pairs, which is a quick way to count. Missing the pairs inside the run 7 7 5 gives 6.
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