Bat Wings

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?

A Mean Tetrahedron

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 faces?

Pairs

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.

Weekly Problem 36 - 2009

Stage: 2 and 3 Short Challenge Level:

The sum of all $64$ numbers is their mean times $64=64^2$. Similarly the sum of the first $36$ numbers is $36^2$. Therefore the sum of the last $28$ numbers is $64^2-36^2=(64+36)(64-36)=100\times 28 = 2800$. Therefore the mean of the last $28$ numbers is $\frac{2800}{28}=100$.

This problem is taken from the UKMT Mathematical Challenges.

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