Here's this week's collection. Answers & extensions tomorrow. Why not discuss the problems on Twitter using #SundayAfternoonMaths.
A piece of string 10cm long is tied to two pins 6cm apart. The string is used to draw an ellipse. The pins are then moved 2cm further apart and a second ellipse is drawn. Which ellipse has the larger area?
Let Tn be the nth triangle number. Find n such that Tn+Tn+1+Tn+2+Tn+3=Tn+4+Tn+5.
Is there a time of day when the hands of an analogue clock (one with a second hand that moves every second instead of moving continuously) will all be 120° apart?