Assume the pattern continues...
- Where would 125 be located?
- Is 125 on a triangle that points up or down?
- Where would 457 be located?
- Is 457 on a triangle that points up or down?

One nice observation is that numerous students, without being prompted, have solved this extension of the problem:
- Where would the positive integer N be located?
- Is the positive integer N on a triangle that points up or down?

Answers to these extensions requires multiple cases, and considerable thought!

Source: Wish I could remember so I could thank the person!

**Hint:** Write out some more cases....Look for patterns.

Do not waste your time (and thinking ability) by extending the pattern visually to 125, or evebn worse, 457!

**Solution Commentary:** Share your answers, observations, and conclusions with others exploring the problem. You can be referees for each other.