Daily Math Puzzle: 2026-07-11
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2026-07-11
A deep-space probe, 'Cosmic Weaver', transmits a sequence of numbers representing unique stellar event signatures it detects. Analyzing the raw data, mission control observes a peculiar, repeating pattern. The sequence received so far is: 1, 2, 3, 5, 4, 7, 8, 9, 11, 10, 13, 14, 15, 17, 16, ? What is the next number in this sequence?
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Solution
19 — The sequence is generated by a repeating pattern that processes consecutive natural numbers (1, 2, 3, 4, 5, 6, ...). Each cycle of the pattern consumes 6 natural numbers and contributes 5 numbers to the observed sequence:
1. **Output 3 in order:** The first three natural numbers (N, N+1, N+2) are output in ascending order.
2. **Output 2 reversed:** The next two natural numbers (N+3, N+4) are output in descending order.
3. **Skip 1:** The sixth natural number (N+5) is skipped entirely and does not appear in the sequence.
The pattern then repeats, starting with N+6 for the next cycle.
Let's break down the given sequence:
- **Cycle 1 (starts with N=1):**
- Output (1, 2, 3) -> The sequence starts: 1, 2, 3
- Output (5, 4) from (4, 5) -> Sequence: 1, 2, 3, 5, 4
- Skip 6.
- **Cycle 2 (starts with N=7):**
- Output (7, 8, 9) -> Sequence: ..., 7, 8, 9
- Output (11, 10) from (10, 11) -> Sequence: ..., 11, 10
- Skip 12.
- **Cycle 3 (starts with N=13):**
- Output (13, 14, 15) -> Sequence: ..., 13, 14, 15
- Output (17, 16) from (16, 17) -> Sequence: ..., 17, 16
- Skip 18.
Following this pattern, the next cycle will start with N=19:
- **Cycle 4 (starts with N=19):**
- The first step is to output the next three consecutive natural numbers (19, 20, 21) in ascending order.
Therefore, the next number in the sequence is 19.
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