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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?

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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.

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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.

Bat Wings

Stage: 3 Challenge Level: Challenge Level:1

The total wingspan for data set A is 6 x 13 = 78 cm so the missing measurement is 78 - 67 = 11 cm.

The total wingspan for data set B is 7 x 14 = 98 cm so the missing measurement is 98 - 84 = 14 cm.

The overall mean is 13.35 cm so the total of all 20 measurements is 20 x 13.35 = 267 cm and the total wingspan for data set C is 267 - (78 + 98) = 91 cm.

The missing measurement for data set C is 91 - 76 = 15 cm and the mean of data set C is 91/7 = 13 cm.