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Bang's Theorem

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

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Rudolff's Problem

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What's it Worth?

Stage: 3 and 4 Challenge Level: Challenge Level:1

If you are a teacher, click here for a version of the problem suitable for classroom use, together with supporting materials. Otherwise, read on...

 

Each symbol has a numerical value. The total for the symbols is written at the end of each row and column.

Can you find the missing total that should go where the question mark has been put?

Grid containing symbols.

 
There's a lot of information in the grid, so you will need to make some choices about what to focus on first. Click below to see some images that draw your attention to particular parts of the grid.

What can you deduce from each image?
 
 
Image 1
 
 
Image 2
 
Image 3
 
Image 4
 
Image 5
 
Image 6
 
Can you find any other ways of solving the problem?
 
 
You can apply these strategies to other versions of the problem. This spreadsheet can be used to generate lots of different examples.
 
 
Here are three other problems that can be solved using similar strategies:
Sweet Shop
Letterland
Children at Large