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?
Can you number the vertices, edges and faces of a tetrahedron so
that the number on each edge is the mean of the numbers on the
adjacent vertices and the mean of the numbers on the adjacent
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.
Snow White wanted to know the mean height of the Seven Dwarves. So one day she measured them all as they left for work and calculated their mean height (correct to one decimal place) as 112.3 cm. Doc complained that she had left him out and measured Dopey twice without him noticing. If Doc is 3 cm taller than Dopey, what is the mean height of the Seven Dwarves?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.