1. Stairs: Investigation
Our office is on the 5th floor and, although there is a lift, I like using the big circular staircase.
I go up the stairs 2 steps at a time but I am annoyed that there is always just 1 step left over when I get to my landing.
One day, in a burst of energy I went up the stairs 3 steps at a time, and still had 1 step left over!
I established that even if I could go up 4, 5 or 6 steps at a time there would still be 1 step left over.

2. Worse yet, no matter how many steps I did at a time (except for 1 or the lot) there would always be some steps left over.
How many steps
are there to our office?
Is there more than one
possible answer?

3. Other possibilities could be 181,241,421,481 or 541. There are more.
Solution:
61 steps.
Other possibilities could be 181,241,421,481 or 541. There are more.
The most likely solution is the 61 steps.