The sequence that changes its rule
A sequence begins 2, 4, 8, 16. You are told the next value is not necessarily 32. Give two valid next values and a clear rule for each. What does this reveal about pattern puzzles?
Pattern challenge at hard difficulty.
Hint
A finite list supports many rules. Prefer rules only when there is evidence for them.
Answer and method
32 is valid under repeated doubling. 31 is also valid if each term is one less than the next power of two after the second term under a suitably defined polynomial or staged rule. Many other answers are possible. Without constraints, a short sequence does not determine one unique continuation.
Reusable reasoning movePattern recognition is hypothesis generation. A puzzle needs constraints to make one hypothesis preferable.