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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?

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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.

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Converging Means

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.

A Mean Tetrahedron

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A tetrahedron has 4 vertices, 6 edges and 4 faces. Can you number them 1 to 14 in such a way that the number on each edge is the mean of the two numbers at the vertices joined by that edge and also the mean of the two numbers on the faces it separates?