One of the talks I usually give is on geometric dissections, which I begin with the following puzzle from (Lindgren 1964):
I thought it might have been more fun to give the puzzle to the prospective audience one week before I actually presented the solution, so I did that for an upcoming presentation on geometric dissections for students from Raffles Girls' School. I hope they got very frustrated by the puzzle. I also promised to give a hint to the puzzle, but I forgot to post it! Highlight the hint if you want to read it...
The cut lies on the grid lines.
Lindgren, Harry (1964). Geometric Dissections. D. Van Nostrand.