Three students had collected some data on the wingspan of some bats. Unfortunately, each student had lost one measurement. Can you find the missing information?
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was thinking of.
Take any two positive numbers. Calculate the arithmetic and geometric means. Repeat the calculations to generate a sequence of arithmetic means and geometric means. Make a note of what happens to the two sequences.
Solutions to this puzzle came in
from Shauneen from Our Lady's Grammar School ,
Newry; Claire and Amy of Madras College, St Andrew's; Nicola and
Rosie of Maidstone Grammar School for Girls and Chris, Sarah, Jack,
Laura, Jan and Michael from Necton Middle School, Norfolk
. An equivalent (dual) solution to the one
illustrated is obtained by swapping the numbers at the vertices
with the numbers on the faces.