In the following series: 6, 4, 1, 2, 2, 8, 7, 4, 2, 1, 5, 3, 8, 6, 2, 2, 7, 1,…
2013
In the following series:
6, 4, 1, 2, 2, 8, 7, 4, 2, 1, 5, 3, 8, 6, 2, 2, 7, 1, 4, 1, 3, 5, 8, 6
How many distinct ordered pairs of successive numbers have an absolute difference of 2? Count repeated occurrences of the same ordered pair only once.
Answer: C. 6 — ConceptIn a sequence, successive numbers occupy neighboring positions. For an adjacent ordered pair (a, b), check the condition |a − b| = 2. Order matters, so…
- A.
4
- B.
5
- C.
6
- D.
8
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Show answer & explanation
Correct answer: C
Concept
In a sequence, successive numbers occupy neighboring positions. For an adjacent ordered pair (a, b), check the condition |a − b| = 2.
Order matters, so (a, b) and (b, a) are different ordered pairs. When distinct pairs are requested, repeated occurrences of the same ordered pair are counted once.
Application
Scan every neighboring pair from left to right and retain only those satisfying |a − b| = 2.
The qualifying occurrences are (6, 4), (4, 2), (5, 3), (8, 6), (1, 3), (3, 5), and (8, 6).
The ordered pair (8, 6) occurs twice, so keep one copy when forming the set of distinct ordered pairs.
Distinct ordered pair | Occurrences |
|---|---|
(6, 4) | 1 |
(4, 2) | 1 |
(5, 3) | 1 |
(8, 6) | 2 |
(1, 3) | 1 |
(3, 5) | 1 |
Cross-check
There are 7 qualifying occurrences in the full scan. Exactly one occurrence is a repeat of (8, 6), so the distinct-pair count is 7 − 1 = 6.
Therefore, the number of distinct ordered adjacent pairs is 6.