Place four pebbles on the sand in the form of a square. Keep adding
as few pebbles as necessary to double the area. How many extra
pebbles are added each time?
Take any whole number between 1 and 999, add the squares of the
digits to get a new number. Make some conjectures about what
happens in general.
Three circles have a maximum of six intersections with each other.
What is the maximum number of intersections that a hundred circles
Good answers to this popular question came from Georgina Baxter,
Suzanne Dash, Emily Savell, Helen Almand, Naomi Pearson, Catherine
Renwick and Sang-mi Kim, Davison High School, Worthing; from James
Dotti and Shabbir Tejani, Jack Hunt School, Peterborough; and from
Rachel Walker, Christianne Eaves, Suzanne Abbott, Peggy Brett,
Fiona Conroy, Nisha Doshi and Helen Battersby, The Mount School,