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Posing extension problems

You pose problems by asking questions. Here are some question openers that often lead to good problems:

What if not (WIN). . . ?
What if . . . ? (What happens if . . . ? What about . . . ?)
Why . . . ?
How many . . . ?
In general, . . . ?
What do we mean by (WDWMB) . . . ?
Is there/Are there . . . ? (Will there be . . . ?)
Is there a relationship . . . ?
Is there a deep similarity between . . . ?
Under what conditions . . . ?
What is/are . . .?
What's the largest/smallest . . . ?
What's an algorithm for . . . ?
What are the properties of . . . ?
What other . . . ?
How do you know . . . ? (Can you prove . . . ? Is it always true that . . . ?)
Is it possible . . . ? (Is it necessarily the case that . . . ? Can you . . . ?)
How can you . . . ?

One example shows how such questions can lead from a very simple problem to some deep mathematics.

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