If you are in need of a good numeracy problem that really draws out learner thinking and sense making - this one has a pretty good hit rate.
I frame this one as a group of mathematicians attempting to track a deadly zombie contagion.
If eight people meet and each shakes hands with the other, how many handshakes are there?
Each handshake represents a point of contact.
The mathematical journey you take as you seek to solve this is a similar journey you would take if you tried to track the movements of a contagion through a population, a computer network, or sports betting formulas.
You will deal with triangular numbers and have to navigate through additive thinking and into multiplicative thinking.
Once you have the solution, take your system and use it to solve for 100 people.
The end result should be a nice formula that elegantly solves the problem.
I beef this problem up by introducing statistics (what if one, two or three people are contagious) and the contagion has a 100, 50 or 25 percent infection rate? You can go on developing the thinking indefinitely. Mortality rate, contagious period, time range within which the infected succumb.
Good luck. I'll reveal the answer and formula in a later post.