Investigation strategies

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.