Three equilateral triangles ABC, AYX and XZB are drawn with the
point X a moveable point on AB. The points P, Q and R are the
centres of the three triangles. What can you say about triangle
PQR?

Water Pistols

Age 16 to 18 Challenge Level:

Your argument has to apply wherever the people are placed. The
result can be proved using mathematical induction but the argument
is quite subtle.