Sunday Afternoon Maths VI

Here's this week's collection. Answers & extensions tomorrow. Why not discuss the problems on Twitter using #SundayAfternoonMaths.

Ellipses

Source: Maths Medicine

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?

Triangle Numbers

Source: ATM Mathematics Teaching 239

Let T_n be the n^th triangle number. Find n such that T_n+T_n+1+T_n+2+T_n+3=T_n+4+T_n+5.

Ticking Clock

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?