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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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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.

Weekly Problem 23 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

112.7 cm.

In order to calculate the mean height, Snow White had to first calculate the sum of the heights of the Dwarves ($S$), and then divide by 7. Her value for $S$ was too small by 3 cm, so her value for the mean was too small by $3/7 \approx 0.4$ cm. So the actual mean height is $112.3+0.4=112.7$ cm.

This problem is taken from the UKMT Mathematical Challenges.

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